Röckner, Michael; Su, Yiming; Zhang, Deng Multi-bubble Bourgain-Wang solutions to nonlinear Schrödinger equations. (English) Zbl 07785455 Trans. Am. Math. Soc. 377, No. 1, 517-588 (2024). MSC: 35Q55 35B44 35B40 35C08 35B25 35R60 PDFBibTeX XMLCite \textit{M. Röckner} et al., Trans. Am. Math. Soc. 377, No. 1, 517--588 (2024; Zbl 07785455) Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Kolmogorov problems on equations for Stationary and transition probabilities of diffusion processes. (English. Russian original) Zbl 07764853 Theory Probab. Appl. 68, No. 3, 342-369 (2023); translation from Teor. Veroyatn. Primen. 68, No. 3, 420-455 (2023). Reviewer: Dejun Luo (Beijing) MSC: 35Q84 35B65 35A01 35A02 35R06 35R60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Theory Probab. Appl. 68, No. 3, 342--369 (2023; Zbl 07764853); translation from Teor. Veroyatn. Primen. 68, No. 3, 420--455 (2023) Full Text: DOI
Röckner, Michael; Su, Yiming; Zhang, Deng Multi solitary waves to stochastic nonlinear Schrödinger equations. (English) Zbl 1517.35090 Probab. Theory Relat. Fields 186, No. 3-4, 813-876 (2023). MSC: 35C08 35Q55 60H15 PDFBibTeX XMLCite \textit{M. Röckner} et al., Probab. Theory Relat. Fields 186, No. 3--4, 813--876 (2023; Zbl 1517.35090) Full Text: DOI arXiv
Barbu, Viorel; Roeckner, Michael The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation. (English) Zbl 1514.35436 Indiana Univ. Math. J. 72, No. 1, 89-131 (2023). MSC: 35Q84 35Q83 35B40 60J65 35R60 PDFBibTeX XMLCite \textit{V. Barbu} and \textit{M. Roeckner}, Indiana Univ. Math. J. 72, No. 1, 89--131 (2023; Zbl 1514.35436) Full Text: DOI arXiv
Bogachev, Vladimir I.; Röckner, Michael; Shaposhnikov, Stanislav V. Zvonkin’s transform and the regularity of solutions to double divergence form elliptic equations. (English) Zbl 1510.35088 Commun. Partial Differ. Equations 48, No. 1, 119-149 (2023). MSC: 35B65 35B09 35J15 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Commun. Partial Differ. Equations 48, No. 1, 119--149 (2023; Zbl 1510.35088) Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Applications of Zvonkin’s transform to stationary Kolmogorov equations. (English. Russian original) Zbl 1506.35056 Dokl. Math. 106, No. 2, 318-321 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 506, 20-24 (2022). MSC: 35J47 35A01 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 106, No. 2, 318--321 (2022; Zbl 1506.35056); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 506, 20--24 (2022) Full Text: DOI
Albeverio, Sergio; Bogachev, Vladimir I.; Röckner, Michael Markov uniqueness and Fokker-Planck-Kolmogorov equations. (English) Zbl 1497.60106 Chen, Zhen-Qing (ed.) et al., Dirichlet forms and related topics, in honor of Masatoshi Fukushima’s beiju, IWDFRT 2022, Osaka, Japan, August 22–26,2022. Singapore: Springer. Springer Proc. Math. Stat. 394, 1-21 (2022). MSC: 60J45 31C25 60J60 35K10 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Springer Proc. Math. Stat. 394, 1--21 (2022; Zbl 1497.60106) Full Text: DOI arXiv
Ren, Panpan; Röckner, Michael; Wang, Feng-Yu Linearization of nonlinear Fokker-Planck equations and applications. (English) Zbl 1486.60104 J. Differ. Equations 322, 1-37 (2022). MSC: 60J60 58J65 60B05 PDFBibTeX XMLCite \textit{P. Ren} et al., J. Differ. Equations 322, 1--37 (2022; Zbl 1486.60104) Full Text: DOI arXiv
Da Prato, Giuseppe; Flandoli, Franco; Röckner, Michael Continuity equation in llogl for the 2D Euler equations under the enstrophy measure. (English) Zbl 1476.35186 Stoch. Partial Differ. Equ., Anal. Comput. 9, No. 2, 491-509 (2021). MSC: 35Q31 60H40 76B03 35A01 35R60 35R06 PDFBibTeX XMLCite \textit{G. Da Prato} et al., Stoch. Partial Differ. Equ., Anal. Comput. 9, No. 2, 491--509 (2021; Zbl 1476.35186) Full Text: DOI arXiv
Bogachev, Vladimir I.; Röckner, Michael; Shaposhnikov, Stanislav V. On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations. (English) Zbl 1474.60185 J. Dyn. Differ. Equations 33, No. 2, 715-739 (2021). MSC: 60J60 35Q84 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Dyn. Differ. Equations 33, No. 2, 715--739 (2021; Zbl 1474.60185) Full Text: DOI arXiv
Röckner, Michael Kolmogorov operators and SPDEs. (English) Zbl 1447.60121 Baake, Michael (ed.) et al., Spectral structures and topological methods in mathematics. Zürich: European Mathematical Society (EMS). EMS Ser. Congr. Rep., 29-53 (2019). MSC: 60H15 PDFBibTeX XMLCite \textit{M. Röckner}, in: Spectral structures and topological methods in mathematics. Zürich: European Mathematical Society (EMS). 29--53 (2019; Zbl 1447.60121) Full Text: DOI
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. On the superposition principle for Fokker-Planck-Kolmogorov equations. (English. Russian original) Zbl 1433.35407 Dokl. Math. 100, No. 1, 363-366 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 487, No. 5, 483-486 (2019). MSC: 35Q84 35R60 60H15 35R06 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 100, No. 1, 363--366 (2019; Zbl 1433.35407); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 487, No. 5, 483--486 (2019) Full Text: DOI
Huang, Xing; Röckner, Michael; Wang, Feng-Yu Nonlinear Fokker-Planck equations for probability measures on path space and path-distribution dependent sdes. (English) Zbl 1417.60056 Discrete Contin. Dyn. Syst. 39, No. 6, 3017-3035 (2019). MSC: 60H15 35Q84 35R06 35R60 60J35 PDFBibTeX XMLCite \textit{X. Huang} et al., Discrete Contin. Dyn. Syst. 39, No. 6, 3017--3035 (2019; Zbl 1417.60056) Full Text: DOI arXiv
Herr, Sebastian; Röckner, Michael; Zhang, Deng Scattering for stochastic nonlinear Schrödinger equations. (English) Zbl 1416.35239 Commun. Math. Phys. 368, No. 2, 843-884 (2019). MSC: 35Q55 35R60 35P25 60J65 PDFBibTeX XMLCite \textit{S. Herr} et al., Commun. Math. Phys. 368, No. 2, 843--884 (2019; Zbl 1416.35239) Full Text: DOI arXiv
Bogachev, Vladimir I.; Röckner, Michael; Shaposhnikov, Stanislav V. Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures. (English) Zbl 1411.60010 J. Funct. Anal. 276, No. 12, 3681-3713 (2019). MSC: 60B10 47G20 60G52 35R06 35K15 60J35 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Funct. Anal. 276, No. 12, 3681--3713 (2019; Zbl 1411.60010) Full Text: DOI arXiv
Barbu, Viorel; Röckner, Michael Global solutions to random 3D vorticity equations for small initial data. (English) Zbl 1409.60094 J. Differ. Equations 263, No. 9, 5395-5411 (2017). MSC: 60H15 35Q30 PDFBibTeX XMLCite \textit{V. Barbu} and \textit{M. Röckner}, J. Differ. Equations 263, No. 9, 5395--5411 (2017; Zbl 1409.60094) Full Text: DOI arXiv
Barbu, Viorel; Röckner, Michael; Zhang, Deng Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case. (English) Zbl 1378.60088 J. Differ. Equations 263, No. 11, 7919-7940 (2017). MSC: 60H15 35Q55 60H30 PDFBibTeX XMLCite \textit{V. Barbu} et al., J. Differ. Equations 263, No. 11, 7919--7940 (2017; Zbl 1378.60088) Full Text: DOI arXiv
Barbu, Viorel; Röckner, Michael; Zhang, Deng The stochastic logarithmic Schrödinger equation. (English. French summary) Zbl 1360.60119 J. Math. Pures Appl. (9) 107, No. 2, 123-149 (2017). Reviewer: Ruhollah Jahanipur (Kashan) MSC: 60H15 47H05 47J05 PDFBibTeX XMLCite \textit{V. Barbu} et al., J. Math. Pures Appl. (9) 107, No. 2, 123--149 (2017; Zbl 1360.60119) Full Text: DOI arXiv
Röckner, Michael; Shin, Jiyong; Trutnau, Gerald Non-symmetric distorted Brownian motion: strong solutions, strong Feller property and non-explosion results. (English) Zbl 1364.31012 Discrete Contin. Dyn. Syst., Ser. B 21, No. 9, 3219-3237 (2016). Reviewer: Sophia L. Kalpazidou (Thessaloniki) MSC: 31C25 60J60 47D07 PDFBibTeX XMLCite \textit{M. Röckner} et al., Discrete Contin. Dyn. Syst., Ser. B 21, No. 9, 3219--3237 (2016; Zbl 1364.31012) Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations. (English) Zbl 1345.35051 J. Funct. Anal. 271, No. 5, 1262-1300 (2016). Reviewer: Stefanie Sonner (Graz) MSC: 35K15 60J60 35Q84 35K55 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Funct. Anal. 271, No. 5, 1262--1300 (2016; Zbl 1345.35051) Full Text: DOI
Barbu, Viorel; Röckner, Michael; Zhang, Deng Stochastic nonlinear Schrödinger equations. (English) Zbl 1336.60118 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 136, 168-194 (2016). MSC: 60H15 35R60 35Q55 35J10 35B65 PDFBibTeX XMLCite \textit{V. Barbu} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 136, 168--194 (2016; Zbl 1336.60118) Full Text: DOI arXiv
Gess, Benjamin; Röckner, Michael Singular-degenerate multivalued stochastic fast diffusion equations. (English) Zbl 1330.60080 SIAM J. Math. Anal. 47, No. 5, 4058-4090 (2015). Reviewer: Martin Ondreját (Praha) MSC: 60H15 60H99 49J40 76S05 PDFBibTeX XMLCite \textit{B. Gess} and \textit{M. Röckner}, SIAM J. Math. Anal. 47, No. 5, 4058--4090 (2015; Zbl 1330.60080) Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Uniqueness problems for degenerate Fokker-Planck-Kolmogorov equations. (English. Russian original) Zbl 1321.35242 J. Math. Sci., New York 207, No. 2, 147-165 (2015); translation from Probl. Mat. Anal. 78, 31-46 (2015). MSC: 35Q84 82C31 35R60 60H20 35A02 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Math. Sci., New York 207, No. 2, 147--165 (2015; Zbl 1321.35242); translation from Probl. Mat. Anal. 78, 31--46 (2015) Full Text: DOI
Bogachev, V. I.; Da Prato, G.; Röckner, M.; Shaposhnikov, S. V. On the uniqueness of solutions to continuity equations. (English) Zbl 1333.35312 J. Differ. Equations 259, No. 8, 3854-3873 (2015). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35R06 35A02 35R60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Differ. Equations 259, No. 8, 3854--3873 (2015; Zbl 1333.35312) Full Text: DOI arXiv
Röckner, Michael; Zhu, Rongchan; Zhu, Xiangchan A note on stochastic semilinear equations and their associated Fokker-Planck equations. (English) Zbl 1308.60079 J. Math. Anal. Appl. 415, No. 1, 83-109 (2014). MSC: 60H15 35R60 35Q84 PDFBibTeX XMLCite \textit{M. Röckner} et al., J. Math. Anal. Appl. 415, No. 1, 83--109 (2014; Zbl 1308.60079) Full Text: DOI arXiv
Da Prato, Giuseppe; Flandoli, Franco; Röckner, Michael Uniqueness for continuity equations in Hilbert spaces with weakly differentiable drift. (English) Zbl 1328.35015 Stoch. Partial Differ. Equ., Anal. Comput. 2, No. 2, 121-145 (2014). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35F10 35A02 58D20 60H07 PDFBibTeX XMLCite \textit{G. Da Prato} et al., Stoch. Partial Differ. Equ., Anal. Comput. 2, No. 2, 121--145 (2014; Zbl 1328.35015) Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. On existence of Lyapunov functions for a stationary Kolmogorov equation with a probability solution. (English. Russian original) Zbl 1339.60083 Dokl. Math. 90, No. 1, 424-428 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 457, No. 2, 136-140 (2014). MSC: 60H30 60H10 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 90, No. 1, 424--428 (2014; Zbl 1339.60083); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 457, No. 2, 136--140 (2014) Full Text: DOI
Barbu, Viorel; Röckner, Michael; Zhang, Deng Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach. (English) Zbl 1300.35116 J. Nonlinear Sci. 24, No. 3, 383-409 (2014). MSC: 35Q41 60H15 35R60 35Q55 PDFBibTeX XMLCite \textit{V. Barbu} et al., J. Nonlinear Sci. 24, No. 3, 383--409 (2014; Zbl 1300.35116) Full Text: DOI
Kolesnikov, Alexander V.; Röckner, Michael On continuity equations in infinite dimensions with non-Gaussian reference measure. (English) Zbl 1317.60083 J. Funct. Anal. 266, No. 7, 4490-4537 (2014). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H30 35R15 35F10 35B45 35L45 46E27 58D20 PDFBibTeX XMLCite \textit{A. V. Kolesnikov} and \textit{M. Röckner}, J. Funct. Anal. 266, No. 7, 4490--4537 (2014; Zbl 1317.60083) Full Text: DOI arXiv
Bogachev, Vladimir I.; Röckner, Michael; Shaposhnikov, Stanislav V. On parabolic inequalities for generators of diffusions with jumps. (English) Zbl 1293.60073 Probab. Theory Relat. Fields 158, No. 1-2, 465-476 (2014). Reviewer: Vivek S. Borkar (Mumbai) MSC: 60J25 60J60 35R09 45K05 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Probab. Theory Relat. Fields 158, No. 1--2, 465--476 (2014; Zbl 1293.60073) Full Text: DOI
Da Prato, G.; Flandoli, F.; Röckner, M. Fokker-Planck equations for SPDE with non-trace-class noise. (English) Zbl 1312.35167 Commun. Math. Stat. 1, No. 3, 281-304 (2013). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 35Q84 60H15 35R60 35Q30 76D05 PDFBibTeX XMLCite \textit{G. Da Prato} et al., Commun. Math. Stat. 1, No. 3, 281--304 (2013; Zbl 1312.35167) Full Text: DOI arXiv
Bogachev, Vladimir I.; Röckner, Michael; Shaposhnikov, Stanislav V. On uniqueness of solutions to the Cauchy problem for degenerate Fokker-Planck-Kolmogorov equations. (English) Zbl 1273.35271 J. Evol. Equ. 13, No. 3, 577-593 (2013). MSC: 35Q84 35K10 35K15 35K65 35K67 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Evol. Equ. 13, No. 3, 577--593 (2013; Zbl 1273.35271) Full Text: DOI
Da Prato, Giuseppe; Röckner, Michael Well posedness of Fokker-Planck equations for generators of time-inhomogeneous Markovian transition probabilities. (English) Zbl 1257.35183 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 23, No. 4, 361-376 (2012). MSC: 35Q84 60J35 47D07 PDFBibTeX XMLCite \textit{G. Da Prato} and \textit{M. Röckner}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 23, No. 4, 361--376 (2012; Zbl 1257.35183) Full Text: DOI
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. On positive and probability solutions to the stationary Fokker-Planck-Kolmogorov equation. (English. Russian original) Zbl 1266.60111 Dokl. Math. 85, No. 3, 350-354 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 444, No. 3, 245-249 (2012). Reviewer: Andrew Dale (Durban) MSC: 60H15 82C31 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 85, No. 3, 350--354 (2012; Zbl 1266.60111); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 444, No. 3, 245--249 (2012) Full Text: DOI
Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. (English) Zbl 1243.60046 J. Math. Anal. Appl. 389, No. 1, 147-164 (2012). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H10 60J60 60H30 PDFBibTeX XMLCite \textit{V. Barbu} et al., J. Math. Anal. Appl. 389, No. 1, 147--164 (2012; Zbl 1243.60046) Full Text: DOI
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. On uniqueness problems related to the Fokker-Planck-Kolmogorov equation for measures. (English. Russian original) Zbl 1291.35425 J. Math. Sci., New York 179, No. 1, 7-47 (2011); translation from Probl. Math. Anal. 61, 9-42 (2011). MSC: 35R06 35A02 35K15 60J60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Math. Sci., New York 179, No. 1, 7--47 (2011; Zbl 1291.35425); translation from Probl. Math. Anal. 61, 9--42 (2011) Full Text: DOI
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. On uniqueness problems related to elliptic equations for measures. (English. Russian original) Zbl 1290.35289 J. Math. Sci., New York 176, No. 6, 759-773 (2011); translation from Probl. Mat. Anal. 58, 47-58 (2011). MSC: 35R06 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Math. Sci., New York 176, No. 6, 759--773 (2011; Zbl 1290.35289); translation from Probl. Mat. Anal. 58, 47--58 (2011) Full Text: DOI
Bogachev, Vladimir; Da Prato, Giuseppe; Röckner, Michael Existence results for Fokker-Planck equations in Hilbert spaces. (English) Zbl 1247.60089 Dalang, Robert C. (ed.) et al., Seminar on stochastic analysis, random fields and applications VI. Centro Stefano Franscini, Ascona, Italy, May 19–23, 2008. Basel: Birkhäuser (ISBN 978-3-0348-0020-4/pbk; 978-3-0348-0021-1/ebook). Progress in Probability 63, 23-35 (2011). MSC: 60H15 60J35 60J60 47D07 PDFBibTeX XMLCite \textit{V. Bogachev} et al., Prog. Probab. 63, 23--35 (2011; Zbl 1247.60089) Full Text: DOI
Bogachev, Vladimir; Da Prato, Giuseppe; Röckner, Michael Uniqueness for solutions of Fokker-Planck equations on infinite dimensional spaces. (English) Zbl 1239.60051 Commun. Partial Differ. Equations 36, No. 4-6, 925-939 (2011). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 60H15 60J35 60J60 47D07 PDFBibTeX XMLCite \textit{V. Bogachev} et al., Commun. Partial Differ. Equations 36, No. 4--6, 925--939 (2011; Zbl 1239.60051) Full Text: DOI arXiv
Barbu, Viorel; Röckner, Michael On a random scaled porous media equation. (English) Zbl 1238.60070 J. Differ. Equations 251, No. 9, 2494-2514 (2011). Reviewer: Maria Gordina (Storrs) MSC: 60H15 35K57 35K59 35R60 PDFBibTeX XMLCite \textit{V. Barbu} and \textit{M. Röckner}, J. Differ. Equations 251, No. 9, 2494--2514 (2011; Zbl 1238.60070) Full Text: DOI
Gess, Benjamin; Liu, Wei; Röckner, Michael Random attractors for a class of stochastic partial differential equations driven by general additive noise. (English) Zbl 1228.35062 J. Differ. Equations 251, No. 4-5, 1225-1253 (2011). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35B41 60H15 37L30 35R60 PDFBibTeX XMLCite \textit{B. Gess} et al., J. Differ. Equations 251, No. 4--5, 1225--1253 (2011; Zbl 1228.35062) Full Text: DOI arXiv
Gordina, Maria; Röckner, Michael; Wang, Feng-Yu Dimension-independent Harnack inequalities for subordinated semigroups. (English) Zbl 1219.43006 Potential Anal. 34, No. 3, 293-307 (2011). Reviewer: Simon Eloshvili (Tbilisi) MSC: 43A80 58J65 60J60 PDFBibTeX XMLCite \textit{M. Gordina} et al., Potential Anal. 34, No. 3, 293--307 (2011; Zbl 1219.43006) Full Text: DOI arXiv
Beyn, Wolf-Jürgen; Gess, Benjamin; Lescot, Paul; Röckner, Michael The global random attractor for a class of stochastic porous media equations. (English) Zbl 1284.60124 Commun. Partial Differ. Equations 36, No. 1-3, 446-469 (2011). MSC: 60H15 35L55 37H10 37L30 37L55 76M35 PDFBibTeX XMLCite \textit{W.-J. Beyn} et al., Commun. Partial Differ. Equations 36, No. 1--3, 446--469 (2011; Zbl 1284.60124) Full Text: DOI arXiv
Bogachev, Vladimir; Da Prato, Giuseppe; Röckner, Michael Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces. (English) Zbl 1239.34063 J. Evol. Equ. 10, No. 3, 487-509 (2010). MSC: 34F05 60H15 34G20 47N30 60J35 60J60 82C70 PDFBibTeX XMLCite \textit{V. Bogachev} et al., J. Evol. Equ. 10, No. 3, 487--509 (2010; Zbl 1239.34063) Full Text: DOI arXiv
Liu, Wei; Röckner, Michael SPDE in Hilbert space with locally monotone coefficients. (English) Zbl 1236.60064 J. Funct. Anal. 259, No. 11, 2902-2922 (2010). Reviewer: Dirk Blömker (Augsburg) MSC: 60H15 35R60 37L55 PDFBibTeX XMLCite \textit{W. Liu} and \textit{M. Röckner}, J. Funct. Anal. 259, No. 11, 2902--2922 (2010; Zbl 1236.60064) Full Text: DOI arXiv
Blanchard, Philippe; Röckner, Michael; Russo, Francesco Probabilistic representation for solutions of an irregular porous media type equation. (English) Zbl 1202.60111 Ann. Probab. 38, No. 5, 1870-1900 (2010). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H30 60H10 60G46 35C99 58J65 PDFBibTeX XMLCite \textit{P. Blanchard} et al., Ann. Probab. 38, No. 5, 1870--1900 (2010; Zbl 1202.60111) Full Text: DOI arXiv
Röckner, Michael; Zhang, Xicheng Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients. (English) Zbl 1202.60112 C. R., Math., Acad. Sci. Paris 348, No. 7-8, 435-438 (2010). Reviewer: Nicolas Perkowski (Berlin) MSC: 60H30 60H10 35A02 35D30 35Q84 PDFBibTeX XMLCite \textit{M. Röckner} and \textit{X. Zhang}, C. R., Math., Acad. Sci. Paris 348, No. 7--8, 435--438 (2010; Zbl 1202.60112) Full Text: DOI
Röckner, Michael; Zhang, Xicheng Tamed 3D Navier – Stokes equation: existence, uniqueness and regularity. (English) Zbl 1180.35417 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 4, 525-549 (2009). MSC: 35Q30 76D05 76D03 PDFBibTeX XMLCite \textit{M. Röckner} and \textit{X. Zhang}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 4, 525--549 (2009; Zbl 1180.35417) Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Nonlinear evolution and transport equations for measures. (English. Russian original) Zbl 1200.35047 Dokl. Math. 80, No. 3, 785-789 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 429, No. 1, 7-11 (2009). Reviewer: Lluís Quer-Sardanyons (Bellaterra) MSC: 35D30 60B10 35F25 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 80, No. 3, 785--789 (2009; Zbl 1200.35047); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 429, No. 1, 7--11 (2009) Full Text: DOI
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Lower estimates of densities of solutions of elliptic equations for measures. (English. Russian original) Zbl 1188.35193 Dokl. Math. 79, No. 3, 329-334 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 2, 156-161 (2009). Reviewer: Henri Schurz (Carbondale) MSC: 35R06 35J25 60H15 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 79, No. 3, 329--334 (2009; Zbl 1188.35193); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 2, 156--161 (2009) Full Text: DOI
Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. (English) Zbl 1162.76054 Ann. Probab. 37, No. 2, 428-452 (2009). MSC: 76S05 76M35 35Q35 PDFBibTeX XMLCite \textit{V. Barbu} et al., Ann. Probab. 37, No. 2, 428--452 (2009; Zbl 1162.76054) Full Text: DOI arXiv
Goldys, Benjamin; Röckner, Michael; Zhang, Xicheng Martingale solutions and Markov selections for stochastic partial differential equations. (English) Zbl 1177.60060 Stochastic Processes Appl. 119, No. 5, 1725-1764 (2009). Reviewer: Isamu Dôku (Saitama) MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{B. Goldys} et al., Stochastic Processes Appl. 119, No. 5, 1725--1764 (2009; Zbl 1177.60060) Full Text: DOI
Bogachev, V. I.; Da Prato, G.; Röckner, M. Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces. (English) Zbl 1161.47027 J. Funct. Anal. 256, No. 4, 1269-1298 (2009). Reviewer: Vincenzo Vespri (Firenze) MSC: 47D07 47N20 35K10 35K57 35R60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Funct. Anal. 256, No. 4, 1269--1298 (2009; Zbl 1161.47027) Full Text: DOI
Bogachev, V. I.; Da Prato, G.; Röckner, M. Parabolic equations for measures on infinite-dimensional spaces. (English. Russian original) Zbl 1221.35442 Dokl. Math. 78, No. 1, 544-549 (2008); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 4, 439-444 (2008). MSC: 35R15 35R06 60H15 47N20 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 78, No. 1, 544--549 (2008; Zbl 1221.35442); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 4, 439--444 (2008) Full Text: DOI
Röckner, Michael; Wang, Feng-Yu Non-monotone stochastic generalized porous media equations. (English) Zbl 1151.76032 J. Differ. Equations 245, No. 12, 3898-3935 (2008). MSC: 76S05 76M35 35Q35 60H15 PDFBibTeX XMLCite \textit{M. Röckner} and \textit{F.-Y. Wang}, J. Differ. Equations 245, No. 12, 3898--3935 (2008; Zbl 1151.76032) Full Text: DOI
Bogachev, V. I.; Da Prato, G.; Röckner, M. Infinite dimensional Kolmogorov operators with time dependent drift coefficients. (English. Russian original) Zbl 1221.60096 Dokl. Math. 77, No. 2, 276-280 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 419, No. 5, 587-591 (2008). Reviewer: A. V. Balakrishnan (Los Angeles) MSC: 60H25 28C20 47D07 60J60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Dokl. Math. 77, No. 2, 276--280 (2008; Zbl 1221.60096); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 419, No. 5, 587--591 (2008) Full Text: DOI
Bogachev, V. I.; Da Prato, G.; Röckner, M. On parabolic equations for measures. (English) Zbl 1323.35058 Commun. Partial Differ. Equations 33, No. 3, 397-418 (2008). MSC: 35K15 35R06 47D07 60J35 60J60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Commun. Partial Differ. Equations 33, No. 3, 397--418 (2008; Zbl 1323.35058) Full Text: DOI
Röckner, Michael; Wang, Feng-Yu Concentration of invariant measures for stochastic generalized porous media equations. (English) Zbl 1152.60048 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10, No. 3, 397-409 (2007). Reviewer: Dominique Lepingle (Orléans) MSC: 60H15 60A10 60J45 35K57 PDFBibTeX XMLCite \textit{M. Röckner} and \textit{F.-Y. Wang}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10, No. 3, 397--409 (2007; Zbl 1152.60048) Full Text: DOI
Ren, Jiagang; Röckner, Michael; Wang, Feng-Yu Stochastic generalized porous media and fast diffusion equations. (English) Zbl 1129.60059 J. Differ. Equations 238, No. 1, 118-152 (2007). MSC: 60H15 76S05 PDFBibTeX XMLCite \textit{J. Ren} et al., J. Differ. Equations 238, No. 1, 118--152 (2007; Zbl 1129.60059) Full Text: DOI arXiv
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael Elliptic equations for measures: regularity and global bounds of densities. (English) Zbl 1206.35242 J. Math. Pures Appl. (9) 85, No. 6, 743-757 (2006). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35R05 35J15 60J60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., J. Math. Pures Appl. (9) 85, No. 6, 743--757 (2006; Zbl 1206.35242) Full Text: DOI
Röckner, Michael; Wang, Feng-Yu; Wu, Liming Large deviations for stochastic generalized porous media equations. (English) Zbl 1155.60313 Stochastic Processes Appl. 116, No. 12, 1677-1689 (2006). MSC: 60F10 35R60 47N20 60H10 PDFBibTeX XMLCite \textit{M. Röckner} et al., Stochastic Processes Appl. 116, No. 12, 1677--1689 (2006; Zbl 1155.60313) Full Text: DOI arXiv
Bogachev, Vladimir I.; Da Prato, Giuseppe; Röckner, Michael; Sobol, Zeev Global gradient bounds for dissipative diffusion operators. (English. Abridged French version) Zbl 1054.60079 C. R., Math., Acad. Sci. Paris 339, No. 4, 277-282 (2004). MSC: 60J35 35J15 60J60 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., C. R., Math., Acad. Sci. Paris 339, No. 4, 277--282 (2004; Zbl 1054.60079) Full Text: DOI
Bogachev, Vladimir I.; Röckner, Michael; Wang, Feng-Yu Invariance implies Gibbsian: some new results. (English) Zbl 1064.53021 Commun. Math. Phys. 248, No. 2, 335-355 (2004). Reviewer: Paweł Walczak (Łódz) MSC: 53C21 53C65 60K35 PDFBibTeX XMLCite \textit{V. I. Bogachev} et al., Commun. Math. Phys. 248, No. 2, 335--355 (2004; Zbl 1064.53021) Full Text: DOI