Julian Toledo's Home Page

Julián Toledo

Julián Toledo & Julián Toledo

Professor
Universitat de València
Dpto. Análisis Matemático

Dirección/Address:
Edificio de Investigación, despacho 3.14
Dr. Moliner 50
46100 Burjassot
Spain

LINKS ON THIS PAGE:
PUBLICATIONS
OTHER LINKS

Docencia:
ver http://www.uv.es/anamat

Publications (Research articles/Books/Other publications)

Research articles

$\blacksquare$ Torsional rigidity in random walk spaces
SIAM J. Math. Anal. 56 (2024), 1604-1642.
https://doi.org/10.1137/23M1553200
J. M. Mazón and J. Toledo

$\blacksquare$ Doubly nonlinear equations for the $1$-Laplacian
J. Evol. Equ. (2023) 23:67, 26 pp.
https://doi.org/10.1007/s00028-023-00917-8
Share link: click here.
J. M. Mazón, A. Molino and J. Toledo

$\blacksquare$ Cahn-Hilliard equations on random walk spaces
Analysis and Applications, Vol. 21, No. 4 (2023) 959-1000.
https:///dx.doi.org/10.1142/S0219530523500045
J. M. Mazón and J. Toledo

$\blacksquare$ Nonlocal doubly nonlinear diffusion problems with nonlinear boundary conditions
J. Evol. Equ. (2023) 23:24, 83 pp.
https://doi.org/10.1007/s00028-022-00854-y
Share link: https://rdcu.be/c664H
M. Solera and J. Toledo

$\blacksquare$ $ (BV,L^p)$-decomposition, $ p=1,2$ , of functions in Metric Random Walk Spaces
Adv. Calc. Var. 15 (2022), no. 3, 515–550.
https://doi.org/10.1515/acv-2020-0011
J. M. Mazón, M. Solera and J. Toledo

$\blacksquare$ Evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in metric random walk spaces
Nonlinear Analysis (2020) 111813, 38 pp.
https://doi.org/10.1016/j.na.2020.111813
J. M. Mazón, M. Solera and J. Toledo

$\blacksquare$ The total variation flow in metric random walk spaces
Calc. Var. 59, 29 (2020), 64 pp.
https://doi.org/10.1007/s00526-019-1684-z
J. M. Mazón, M. Solera and J. Toledo

$\blacksquare$ The heat flow on metric random walk spaces
J. Math. Anal. Appl. 483 (2020) 123645, 53 pp.
https://doi.org/10.1016/j.jmaa.2019.123645
J. M. Mazón, M. Solera and J. Toledo

$\blacksquare$ Nonlocal perimeter, curvature and minimal surfaces for measurable sets
Journal d'Analyse Mathématique 138 (2019), 235-279.
https://doi.org/doi:%2010.1007/s11854-019-0027-5
Share link: https://rdcu.be/bIxmm
J. M. Mazón, J. D. Rossi and J.Toledo

$\blacksquare$ Optimal mass transportation for costs given by Finsler distances via $p$-Laplacian approximations
Adv. Calc. Var. 2018; 11(1): 1-28.
https://doi.org/10.1515/acv-2015-0052
J. M. Mazón, N. Igbida, J. D. Rossi and J. Toledo

$\blacksquare$ An optimal matching problem with constrains
Rev Mat Complut (2018) 31: 407-447.
https://doi.org/10.1007/s13163-018-0256-7
J. M Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ On the uniqueness and numerical approximations for a matching problem
SIAM J. OPTIM. 27 (2017) 2459-2480.
https://doi.org/10.1137/16M1105001
N. Igbida, V. T. Nguyen and J. Toledo

$\blacksquare$ The Heat Content for Nonlocal Diffusion with Non-singular Kernels
Advanced Nonlinear Studies 17 (2017), 255-268.
https://doi.org/10.1515/ans-2017-0005
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Fractional $p$- Laplacian evolution equations (click)
J. Math. Pures Appl. 105 (2016), 810-844.
https://doi.org/10.1016/j.matpur.2016.02.004
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ A nonlocal $1$-Laplacian and median values (click)
Publ. Mat. 60 (2016), 27-53.
https://doi.org/10.5565/PUBLMAT_60116_02
J. M. Mazón, M. Pérez-Llanos, J. D. Rossi and J. Toledo

$\blacksquare$ Optimal mass transport on metric graphs (click)
SIAM J. Optim. 28 (2015), 1609-1632
https://doi.org/10.1137/140995611
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Optimal matching problems with costs given by Finsler distances (click)
Communications on Pure and Applied Analysis 14 (2015), 229-244.
https://doi.org/10.3934/cpaa.2015.14.229
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ On optimal matching measures for matching problems related to the Euclidean distance (click)
Mathematica Bohemica 139 (2014), 553-566.
https://dml.cz/handle/10338.dmlcz/144132
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Mass transport problems obtained as limits of $p$-Laplacian type problems with spatial dependence (click)
Adv. Nonlinear Anal. 3 (2014), 133-140.
https://doi.org/10.1515/anona-2013-0022
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Mass transport problems for the Euclidean distance obtained as limits of $p$-Laplacian type problems with obstacles (click)
J Differential Equations 256 (2014), 3208-3244.
https://doi.org/10.1016/j.jde.2014.01.039
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ An optimal matching problem for the Euclidean distance (click)
SIAM J. Math. Anal. 46 (2014), 233-255.
https://doi.org/10.1137/120901465
J. M. Mazón J. D. Rossi and J. Toledo

$\blacksquare$ An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary (click)
Rev. Mat. Iberoam. 30 (2014), no. 1, 277-308.
https://doi.org/10.4171/rmi/778
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ On the best Lipschitz extension problem for a discrete distance and the discrete infinity-Laplacian (click)
J. Math. Pures Appl. (9) 97 (2012), no. 2, 98-119.
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ A Monge-Kantorovich mass transport problem for a discrete distance (click)
J. Funct. Anal. 260 (2011), 3494–3534.
N. Igbida, J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Local and nonlocal weighted $p$-laplacian evolution equations with Neumann boundary conditions (click)
Publ. Mat. 55 (2011), 27-66.
F. Andreu, J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Degenerate elliptic equations with nonlinear boundary conditions and measures data (click)
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), no. 4, 767–803.
Andreu, Fuensanta; Igbida, Noureddine; Mazón, José M.; Toledo, Julián

$\blacksquare$ The limit as $p\to ∞$ in a nonlocal $p$-Laplacian evolution equation: a nonlocal approximation of a model for sandpiles (click)
Calc. Var. Partial Differential Equations 35 (2009), no. 3, 279–316.
Andreu, F.; Mazón, J. M.; Rossi, J. D.; Toledo, J.

$\blacksquare$ A nonlocal $p$-Laplacian evolution equation with nonhomogeneous Dirichlet boundary conditions (click)
SIAM J. Math. Anal. 40 (2008/09), no. 5, 1815–1851.
Andreu, F.; Mazón, J. M.; Rossi, J. D.; Toledo, J.

$\blacksquare$ Obstacle problems for degenerate elliptic equations with nonhomogeneous nonlinear boundary conditions (click)
Math. Models Methods Appl. Sci. 18 (2008), no. 11, 1869–1893.
Andreu, Fuensanta; Igbida, Noureddine; Mazón, José M.; Toledo, Julián

$\blacksquare$ A nonlocal $p$-Laplacian evolution equation with Neumann boundary conditions (click)
J. Math. Pures Appl. (9) 90(2008), no. 2, 201–227.
Andreu, F.; Mazón, J. M.; Rossi, J. D.; Toledo, J.

$\blacksquare$ Renormalized solutions for degenerate elliptic-parabolic problems with nonlinear dynamical boundary conditions and $L^1$-data (click)
J. Differential Equations 244 (2008), no. 11, 2764–2803.
Andreu, F.; Igbida, N.; Mazón, J. M.; Toledo, J.

$\blacksquare$ The Neumann problem for nonlocal nonlinear diffusion equations (click)
J. Evol. Equ. 8 (2008), no. 1,189–215.
Andreu, Fuensanta; Mazón, José M.; Rossi, Julio D.; Toledo, Julián

$\blacksquare$ $L^1$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions (click)
Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 1, 61–89.
Andreu, F.; Igbida, N.; Mazón, J. M.; Toledo, J.

$\blacksquare$ Quasi-linear elliptic problems in $L^1$ with non homogeneous boundary conditions (click)
Rend. Mat. Appl. (7) 26 (2006), no. 3-4, 291–314.
Ammar, K.; Andreu, F.; Toledo, J.

$\blacksquare$ A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions (click)
Interfaces Free Bound. 8 (2006),no. 4, 447–479.
Andreu, F.; Mazón, J. M.; Toledo, J.; Igbida, N.

$\blacksquare$ Quasi-linear diffusion equations with gradient terms and $L^1$ data (click)
Nonlinear Anal. 56 (2004), no. 8, 1175–1209.
Andreu, F.; Segura de León, S.; Toledo, J.

$\blacksquare$ Blow-up for a class of nonlinear parabolic problems (click)
Asymptot. Anal. 29 (2002), no. 2, 143–155.
Andreu, F.; Mazón, J. M.; Simondon, F.; Toledo, J.

$\blacksquare$ Porous medium equation with absorption and a nonlinear boundary condition (click)
Nonlinear Anal. 49 (2002), no. 4, Ser. A: Theory Methods, 541–563.
Andreu, F.; Mazón, J. M.; Toledo, J.; Rossi, J. D.

$\blacksquare$ Regularity for entropy solutions of parabolic $p$-Laplacian type equations (click)
Publ. Mat. 43 (1999), no. 2, 665–683.
Segura de León, S.; Toledo, J.

$\blacksquare$ Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source (click)
Math. Ann.314 (1999), no. 4, 703–728.
Andreu, F.; Mazón, J. M.; Simondon, F.; Toledo, J.

$\blacksquare$ Existence and uniqueness for a degenerate parabolic equation with $L^1$-data (click)
Trans. Amer. Math. Soc. 351 (1999), no. 1, 285–306.
Andreu, F.; Mazón, J. M.; Segura de León, S.; Toledo, J.

$\blacksquare$ Asymptotic behaviour of solutions of quasi-linear parabolic equations with nonlinear flux (click)
Comput. Appl. Math. 17 (1998),no. 2, 201–215.
Andreu, F.; Mazón, J. M.; Toledo, J.

$\blacksquare$ Attractor for a degenerate nonlinear diffusion problem with nonlinear boundary condition (click)
J. Dynam. Differential Equations 10 (1998), no. 3, 347–377.
Andreu, F.; Mazón, J. M.; Simondon, F.; Toledo, J.

$\blacksquare$ Quasi-linear elliptic and parabolic equations in $L^1$ with nonlinear boundary conditions (click)
Adv. Math. Sci. Appl. 7(1997), no. 1, 183–213.
Andreu, F.; Mazón, J. M.; Segura de León, S.; Toledo, J.

$\blacksquare$ Large-time behavior of solutions of a system of PDE's governing diffusion processes in a heterogeneous medium (click)
Differential Integral Equations 10 (1997), no. 1, 165–180.
Mazón, José M.; Toledo, Julián

$\blacksquare$ Stabilization of solutions of the filtration equation in $\mathbb{R}^N$ (click)
Houston J. Math. 22 (1996), no. 1, 183–198.
Mazón, J. M.; Toledo, J.

$\blacksquare$ Stabilization of solutions of the filtration equation with absorption and non-linear flux (click)
NoDEA Nonlinear Differential Equations Appl. 2 (1995), no. 3, 267–289.
Andreu, F.; Mazón, J. M.; Toledo, J.

$\blacksquare$ Asymptotic behaviour of solutions of the filtration equation in bounded domains
Dynam. Systems Appl. 3 (1994), no. 2, 275–295.
Mazón, José M.; Toledo, Julián

Books and Chapters

$\blacksquare$ Variational and Diffusion Problems in Random Walk Spaces
Cover
Series:Progress in Nonlinear Differential Equations and Their Applications, Vol. 103, Birkhäuser, 2023.
José M. Mazón, Marcos Solera Diana, J. Julián Toledo-Melero
https://link.springer.com/book/9783031335839

$\blacksquare$ Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets
Cover
Series:Frontiers in Mathematics, Birkhäuser, 2019
Mazón, José M., Rossi Julio D., Toledo, J. Julián
https://www.springer.com/gb/book/9783030062422

$\blacksquare$ Nonlocal Diffusion Problems (click)
Cover
Mathematical Surveys and Monographs, vol. 165. AMS, 2010.
Fuensanta Andreu-Vaillo, José M. Mazón, Julio D. Rossi, and J. Toledo-Melero

$\blacksquare$ Degenerate Elliptic Equations with Nonlinear Boundary Conditions
Cover
Chapter in On the notions of solution to nonlinear elliptic problems: results and developments. pp 67-104. (click)
Quaderni di matematica, vol. 23 (2009).
Edited by A. Alvino, A. Mercaldo, F. Murat and I. Peral.
F. Andreu, N. Igbida, J. M. Mazón and J. Toledo

Proceedings and surveys

$\blacksquare$ Gradient flows in metric random walk spaces
SeMA J. 79 (2022), no. 1, 3–35.
https://doi.org/10.1007/s40324-021-00272-z
J. M. Mazón, M. Solera and J. Toledo

$\blacksquare$ On Nonlinear Nonlocal Diffusion Problems (Survey)
International Journal of Biomathematics and Biostatistics 1 (2010), no. 3, 191-202.
J. M. Mazón, J. D. Rossi and J. Toledo

$\blacksquare$ Existence and uniqueness results for quasi-linear elliptic and parabolic equations with nonlinear boundary conditions
Free boundary problems, 11–21, Internat. Ser. Numer. Math., 154, Birkhäuser, Basel, 2007.
Andreu, F.; Igbida, N.; Mazón, J. M.; Toledo, J.

$\blacksquare$ Attractor for a degenerate nonlinear parabolic equation with a nonlinear flux
Proceedings of the IV Catalan Days of Applied Mathematics (Tarragona, 1998), 1–7, Univ. Rovira Virgili, Tarragona, 1998.
Andreu, F.; Mazon, J. M.; Toledo, J.; Simondon, F.

$\blacksquare$ Entropy solutions for a degenerated parabolic equation
Proceedings of the 3rd Catalan Days on Applied Mathematics (Lleida, 1996), 151–161, Univ. Lleida, Lleida.
Andreu, F.; Mazon, J. M.; Segura, S.; Toledo, J.

$\blacksquare$ Els inicis de la matemàtica moderna (Science outreach)
Chapter in ELS ORIGENS.
Monografies de les Seccions de Ciències, 11 (1994).
Universitat Catalana d’Estiu.
Institut d’Estudis Catalans.
J. Julià Toledo

Some links

Talks

A conference on Non Local Problems

A conference on Optimal Mass Transport Problems from $p$-Laplacian type Problems (Workshop on nonlinear equations, University Carlos III, Madrid, 2013)

A conference on Limit cases of nonlocal problems with Dirichlet boundary conditions (5th Iberian Mathematical Meeting, University of Aveiro, 2014)

5ème Ecole de Printemps EDP Non-Linéaire. Mathématiques et Interactions: modèles non locaux et applications.
Ecole Supérieure de Technologie d'Essaouira, du 27 au 30 Avril 2015.
http://www.este.ucam.ac.ma/EPEDPNL2015/Ecole
Courses by:
Jérôme Coville
Abderrahim El Moataz Billah
Espen Robstad Jakobsen
Grzegorz Karch
Julián Toledo (click)

A conference on A PDE approach to optimal matching problems (VI jornadas de Análisis Matemático, University of Alicante, 2018)

Conferences

Remembering Fuensanta Andreu
A conference in memoriam: http://www.uv.es/edpnol/fuensanta/
http://www.ams.org/mathscinet-getitem?mr=2512556

Nonlinear Partial Differential Equations
A congress on the occasion of J.M. Mazón's 60th birthday
Burjassot (Valencia) from 01/07/2013 to 05/07/2013.

Conference: Partial Differential Equations in Valencia
http://edpnol.blogs.uv.es/

Colleagues web pages

Jesús García's Home Page
Noureddine Igbida’s Home Page
José M. Mazón’s Home Page
Julio D. Rossi’s Home Page

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