del Teso, Félix; Gómez-Castro, David; Vázquez, Juan Luis Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas. (English) Zbl 1498.35570 Fract. Calc. Appl. Anal. 24, No. 4, 966-1002 (2021). MSC: 35R11 35J60 35J92 26A33 PDFBibTeX XMLCite \textit{F. del Teso} et al., Fract. Calc. Appl. Anal. 24, No. 4, 966--1002 (2021; Zbl 1498.35570) Full Text: DOI arXiv
Vázquez, Juan Luis The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case. (English) Zbl 1471.35312 Calc. Var. Partial Differ. Equ. 60, No. 4, Paper No. 140, 59 p. (2021). MSC: 35R11 35K15 35K92 35K65 35A08 35B06 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Calc. Var. Partial Differ. Equ. 60, No. 4, Paper No. 140, 59 p. (2021; Zbl 1471.35312) Full Text: DOI arXiv Backlinks: MO
del Teso, Félix; Gómez-Castro, David; Vázquez, Juan Luis Estimates on translations and Taylor expansions in fractional Sobolev spaces. (English) Zbl 1462.46038 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 200, Article ID 111995, 11 p. (2020). MSC: 46E35 26D10 PDFBibTeX XMLCite \textit{F. del Teso} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 200, Article ID 111995, 11 p. (2020; Zbl 1462.46038) Full Text: DOI arXiv
Vázquez, J. L. The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour. (English) Zbl 1447.35205 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 199, Article ID 112034, 31 p. (2020). MSC: 35K92 35K65 35R11 35A08 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 199, Article ID 112034, 31 p. (2020; Zbl 1447.35205) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Existence of weak solutions for a general porous medium equation with nonlocal pressure. (English) Zbl 1437.35430 Arch. Ration. Mech. Anal. 233, No. 1, 451-496 (2019). Reviewer: Piotr Biler (Wrocław) MSC: 35K55 35Q35 35R11 35D30 35B45 PDFBibTeX XMLCite \textit{D. Stan} et al., Arch. Ration. Mech. Anal. 233, No. 1, 451--496 (2019; Zbl 1437.35430) Full Text: DOI arXiv
Díaz, J. I.; Gómez-Castro, D.; Vázquez, J. L. The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach. (English) Zbl 1402.35093 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 177, Part A, 325-360 (2018). MSC: 35J10 35D30 35J67 35J75 35R11 PDFBibTeX XMLCite \textit{J. I. Díaz} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 177, Part A, 325--360 (2018; Zbl 1402.35093) Full Text: DOI arXiv
Vázquez, Juan Luis Asymptotic behaviour for the fractional heat equation in the Euclidean space. (English) Zbl 1388.35216 Complex Var. Elliptic Equ. 63, No. 7-8, 1216-1231 (2018). MSC: 35R11 35K55 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Complex Var. Elliptic Equ. 63, No. 7--8, 1216--1231 (2018; Zbl 1388.35216) Full Text: DOI arXiv
Vázquez, Juan Luis The mathematical theories of diffusion: nonlinear and fractional diffusion. (English) Zbl 1492.35151 Bonforte, Matteo (ed.) et al., Nonlocal and nonlinear diffusions and interactions: new methods and directions. Cetraro, Italy, July 4–8, 2016. Lecture notes given at the course. Cham: Springer; Florence: Fondazione CIME. Lect. Notes Math. 2186, 205-278 (2017). MSC: 35K57 35R11 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Lect. Notes Math. 2186, 205--278 (2017; Zbl 1492.35151) Full Text: DOI arXiv
Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis Optimal existence and uniqueness theory for the fractional heat equation. (English) Zbl 1364.35416 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 153, 142-168 (2017). MSC: 35R11 35A01 35A02 35K05 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 153, 142--168 (2017; Zbl 1364.35416) Full Text: DOI arXiv
Vázquez, Juan Luis The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation. (English) Zbl 1348.35042 J. Differ. Equations 260, No. 7, 6038-6056 (2016). Reviewer: Vladimir N. Grebenev (Darmstadt) MSC: 35B45 35B65 35K55 35K65 35R11 PDFBibTeX XMLCite \textit{J. L. Vázquez}, J. Differ. Equations 260, No. 7, 6038--6056 (2016; Zbl 1348.35042) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Finite and infinite speed of propagation for porous medium equations with nonlocal pressure. (English) Zbl 1379.35253 J. Differ. Equations 260, No. 2, 1154-1199 (2016). MSC: 35Q35 35K65 76S05 35R11 PDFBibTeX XMLCite \textit{D. Stan} et al., J. Differ. Equations 260, No. 2, 1154--1199 (2016; Zbl 1379.35253) Full Text: DOI arXiv
Carrillo, José Antonio; Vázquez, Juan Luis Some free boundary problems involving non-local diffusion and aggregation. (English) Zbl 1353.35320 Philos. Trans. A, R. Soc. Lond. 373, No. 2050, Article ID 20140275, 16 p. (2015). MSC: 35R35 35R11 35S30 47F05 PDFBibTeX XMLCite \textit{J. A. Carrillo} and \textit{J. L. Vázquez}, Philos. Trans. A, R. Soc. Lond. 373, No. 2050, Article ID 20140275, 16 p. (2015; Zbl 1353.35320) Full Text: DOI arXiv
Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. (English) Zbl 1347.35129 Discrete Contin. Dyn. Syst. 35, No. 12, 5725-5767 (2015). Reviewer: Vladimir N. Grebenev (Darmstadt) MSC: 35K55 35K61 35K65 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Discrete Contin. Dyn. Syst. 35, No. 12, 5725--5767 (2015; Zbl 1347.35129) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Transformations of self-similar solutions for porous medium equations of fractional type. (English) Zbl 1383.35248 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 119, 62-73 (2015). MSC: 35R11 35C06 35K65 76S05 PDFBibTeX XMLCite \textit{D. Stan} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 119, 62--73 (2015; Zbl 1383.35248) Full Text: DOI arXiv
Carrillo, J. A.; Huang, Y.; Santos, M. C.; Vázquez, J. L. Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure. (English) Zbl 1307.35311 J. Differ. Equations 258, No. 3, 736-763 (2015). MSC: 35R11 35K55 35K65 26A33 76S05 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., J. Differ. Equations 258, No. 3, 736--763 (2015; Zbl 1307.35311) Full Text: DOI arXiv
Vázquez, Juan-Luis Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators. (English) Zbl 1290.26010 Discrete Contin. Dyn. Syst., Ser. S 7, No. 4, 857-885 (2014). MSC: 26A33 35K55 35K65 35S10 PDFBibTeX XMLCite \textit{J.-L. Vázquez}, Discrete Contin. Dyn. Syst., Ser. S 7, No. 4, 857--885 (2014; Zbl 1290.26010) Full Text: DOI arXiv
Lu, Peng; Ni, Lei; Vázquez, Juan-Luis; Villani, Cédric Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. (English) Zbl 1156.58015 J. Math. Pures Appl. (9) 91, No. 1, 1-19 (2009). MSC: 58J90 35Q72 PDFBibTeX XMLCite \textit{P. Lu} et al., J. Math. Pures Appl. (9) 91, No. 1, 1--19 (2009; Zbl 1156.58015) Full Text: DOI arXiv