Łasica, Michaeł; Rybka, Piotr Existence of \(W^{1,1}\) solutions to a class of variational problems with linear growth on convex domains. (English) Zbl 1482.35060 Indiana Univ. Math. J. 70, No. 6, 2427-2450 (2021). MSC: 35B65 35J20 35J62 35J70 35J75 PDFBibTeX XMLCite \textit{M. Łasica} and \textit{P. Rybka}, Indiana Univ. Math. J. 70, No. 6, 2427--2450 (2021; Zbl 1482.35060) Full Text: DOI arXiv
Giga, Yoshikazu; Nakayashiki, Ryota; Rybka, Piotr; Shirakawa, Ken On boundary detachment phenomena for the total variation flow with dynamic boundary conditions. (English) Zbl 1450.35147 J. Differ. Equations 269, No. 12, 10587-10629 (2020). MSC: 35K67 35K65 35K20 35A21 35A15 PDFBibTeX XMLCite \textit{Y. Giga} et al., J. Differ. Equations 269, No. 12, 10587--10629 (2020; Zbl 1450.35147) Full Text: DOI arXiv
Giga, Yoshikazu; Muszkieta, Monika; Rybka, Piotr A duality based approach to the minimizing total variation flow in the space \(H^{-s}\). (English) Zbl 1410.94006 Japan J. Ind. Appl. Math. 36, No. 1, 261-286 (2019). MSC: 94A08 65M06 49N90 35K25 PDFBibTeX XMLCite \textit{Y. Giga} et al., Japan J. Ind. Appl. Math. 36, No. 1, 261--286 (2019; Zbl 1410.94006) Full Text: DOI arXiv
Nakayasu, Atsushi; Rybka, Piotr Integrability of the derivative of solutions to a singular one-dimensional parabolic problem. (English) Zbl 1407.35120 Topol. Methods Nonlinear Anal. 52, No. 1, 239-257 (2018). MSC: 35K65 35K67 PDFBibTeX XMLCite \textit{A. Nakayasu} and \textit{P. Rybka}, Topol. Methods Nonlinear Anal. 52, No. 1, 239--257 (2018; Zbl 1407.35120) Full Text: DOI arXiv Euclid
Górny, Wojciech; Rybka, Piotr; Sabra, Ahmad Special cases of the planar least gradient problem. (English) Zbl 1354.49001 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 151, 66-95 (2017). MSC: 49J10 49Q10 49J20 35A15 PDFBibTeX XMLCite \textit{W. Górny} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 151, 66--95 (2017; Zbl 1354.49001) Full Text: DOI arXiv
Giga, Yoshikazu; Górka, Przemysław; Rybka, Piotr Bent rectangles as viscosity solutions over a circle. (English) Zbl 1325.53085 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 518-549 (2015). MSC: 53C44 35K55 35D40 35B51 PDFBibTeX XMLCite \textit{Y. Giga} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 518--549 (2015; Zbl 1325.53085) Full Text: DOI Link
Giga, M.-H.; Giga, Y.; Rybka, P. A comparison principle for singular diffusion equations with spatially inhomogeneous driving force for graphs. (English) Zbl 1288.35137 Arch. Ration. Mech. Anal. 211, No. 2, 419-453 (2014); erratum ibid. 212, No. 2, 707 (2014). Reviewer: Cristian Chifu (Cluj-Napoca) MSC: 35B51 35K65 35D40 35K59 PDFBibTeX XMLCite \textit{M. H. Giga} et al., Arch. Ration. Mech. Anal. 211, No. 2, 419--453 (2014; Zbl 1288.35137) Full Text: DOI
Mucha, Piotr Bogusław; Rybka, Piotr Well posedness of sudden directional diffusion equations. (English) Zbl 1280.35070 Math. Methods Appl. Sci. 36, No. 17, 2359-2370 (2013). MSC: 35K65 35K67 35A01 35K20 35B65 35B05 PDFBibTeX XMLCite \textit{P. B. Mucha} and \textit{P. Rybka}, Math. Methods Appl. Sci. 36, No. 17, 2359--2370 (2013; Zbl 1280.35070) Full Text: DOI arXiv
Kielak, Karolina; Mucha, Piotr Bogusław; Rybka, Piotr Almost classical solutions to the total variation flow. (English) Zbl 1263.35148 J. Evol. Equ. 13, No. 1, 21-49 (2013). MSC: 35K67 74N05 94A08 35K59 35K65 PDFBibTeX XMLCite \textit{K. Kielak} et al., J. Evol. Equ. 13, No. 1, 21--49 (2013; Zbl 1263.35148) Full Text: DOI arXiv
Mucha, Piotr Bogusław; Rybka, Piotr A note on a model system with sudden directional diffusion. (English) Zbl 1245.82020 J. Stat. Phys. 146, No. 5, 975-988 (2012). Reviewer: Utkir Rozikov (Tashkent) MSC: 82B26 PDFBibTeX XMLCite \textit{P. B. Mucha} and \textit{P. Rybka}, J. Stat. Phys. 146, No. 5, 975--988 (2012; Zbl 1245.82020) Full Text: DOI