Publications

dT, F; Medina, M.; Ochoa, P. Higher-order asymptotic expansions and finite difference schemes for the fractional p-Laplacian. Math. Ann. (online ready) (2023)  Preprint: Journal / arXiv

dT, F.; Lindgren, E. Finite difference methods for the parabolic p-Laplace equation. SeMA Journal. 80  (2023), 527–547 (2023) Journal / arXiv 

dT, F; Endal, J.; Jakobsen, E.R., Vázquez, J.L. Evolution driven by the infinity fractional Laplacian.  Calc. Var. PDE.  62(4) (2023), no. 136. Journal / arXiv 

dT, F.; Endal, J.; Jakobsen, E. R.  Uniform tail estimates and $L^p(R^N)$-convergence for finite-difference approximations of nonlinear diffusion equations.  Discrete Contin. Dyn. Syst. 43 (2023), no.3&4, 1319-1346.  Journal / arXiv 

dT, F.; Manfredi, J. J.;  Parviainen, M. Convergence of dynamic programming principles for the p-Laplacian.   Adv. Calc. Var.  15 (2022), no. 2, 191-212. Journal / arXiv.

dT, F.; Lindgren, E.  A finite difference method  for the variational p-Laplacian.  Journal of Scientific Computing. 90 (2022), no. 67, 31 pp Journal / arXiv.

dT, F.; Endal, J; Lewicka, M. On asymptotic expansions for the fractional infinity Laplacian. Asymptotic Analysis 127 (2022), no. 3, 201-216 Journal / arXiv.

dT, F.; Gómez-Castro, D. ; Vázquez, J. L. Three representations of the fractional p-Laplacian: semigroup, extension and Balakrishnan formulas.   Fractional Calculus and Applied Analysis. 24 (2021), no. 4,  996-1002. Journal / arXiv.

dT, F.; Lindgren, E. A mean value formula for the variational p-Laplacian. (2021).    NoDEA Nonlinear Differential Equations Appl. 28 (2021), no. 3, 1-27. Journal / arXiv.

dT, F.; Endal, J.; Vázquez, J. L. The one-phase fractional Stefan problem. Math. Models Methods Appl. Sci.  31 (2021), no.1, 83-131.  Journal / arXiv.

Alibaud, N.; dT, F.; Endal, J.; Jakobsen, E. R. The Liouville theorem and linear operators satisfying the maximum principle. J. Math. Pures Appl. 142 (2020) 229–242 . Journal / arXiv.

dT, F.; Gómez-Castro, D. ; Vázquez, J. L. Estimates on translations and Taylor expansions in fractional Sobolev spaces.  Nonlinear Anal. 200  (2020). Preprint: Journal / arXiv.

dT, F.; Endal, J.; Vázquez, J. L. On the two-phase fractional Stefan problem.  Adv. Nonlinear Stud. 20 (2020), no. 2, 437–458. Journal / arXiv.

Cusimano, N.; dT, F.; Gerardo-Giorda, L. Numerical approximations for fractional elliptic equations via the method of semigroups.  ESAIM Math. Model. Numer. Anal. 54 (2020), no. 3, 751–774.  Journal / arXiv.

dT, F.; Endal, J.; Jakobsen, E. R. Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory.   SIAM J. Numer. Anal.  57 (2019), no. 5, 2266–2299.   Journal / arXiv.

Stan, D.; dT, F.;  Vázquez, J. L. Existence of weak solutions for a general porous medium equation with nonlocal pressure. Arch. Ration. Mech. Anal. 233 (2019), no. 1, 451-496.  Journal / arXiv.

dT, F.; Endal, J.; Jakobsen, E. R. Robust numerical methods for nonlocal (and) equations of porous medium type. Part II: Schemes and experiments. SIAM J. Numer. Anal. 56 (2018), no. 6, 3611–3647. Journal / arXiv. 

Cusimano, N.; dT, F.; Gerardo-Giorda, L.; Pagnini, G. Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions. SIAM J. Numer. Anal. 56 (2018), no. 3, 1243–1272. Journal / arXiv.

dT, F.; Endal, J.; Jakobsen, E. R. Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type. Adv. Math. 305 (2017), 78–143. Journal / arXiv.

dT, F.; Endal, J.; Jakobsen, E. R. On distributional solutions of local and nonlocal problems of porous medium type. C. R. Math. Acad. Sci. Paris 355 (2017), no. 11,1154–1160.  Journal / arXiv.

Stan, D.; dT, F.;  Vázquez, J. L. Finite and infinite speed of propagation for porous medium equations with nonlocal pressure. J. Differential Equations 260 (2016), no. 2, 1154–1199. Journal / arXiv.

Stan, D.; dT, F.;  Vázquez, J. L. Transformations of self-similar solutions for porous medium equations of fractional type. Nonlinear Anal. 119 (2015), 62–73. Journal / arXiv.

Stan, D.; dT, F.;  Vázquez, J. L. Finite and infinite speed of propagation for porous medium equations with fractional pressure. C. R. Math. Acad. Sci. Paris 352 (2014), no. 2, 123–128. Journal / arXiv.

dT, F. Finite difference method for a fractional porous medium equation. Calcolo 51 (2014), no. 4, 615–638. Journal / arXiv.

dT, F.; Endal, J.; Jakobsen, E. R. On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type. Non-linear partial differential equations, mathematical physics, and stochastic analysis, 129–167, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2018.  Publication / arXiv.

Stan, D.; dT, F.;  Vázquez, J. L. Porous medium equation with nonlocal pressure. Current research in nonlinear analysis, 277–308, Springer Optim. Appl., 135,Springer, Cham, 2018.  Publication / arXiv.

dT, F; Jakobsen, E. R. A convergent finite difference-quadrature scheme for the porous medium equation with nonlocal pressure. 2023. Preprint: arXiv

dT, F; Płociniczak,  Ł. Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations. 2023.  Preprint: arXiv

Alibaud, Nathael (Univ. of Bourgogne Franche-Comté, France)

Cusimano, Nicole (Basque Center for Applied Mathematics, Spain)

Endal, Jørgen (Norwegian Univ. of Science and Technology, Norway)

Gerardo-Giorda, Luca (Basque Center for Applied Mathematics, Spain)

Gómez-Castro, David (Univ. Complutense de Madrid, Spain)

Jakobsen, Espen (Norwegian Univ. of Science and Technology, Norway)

Lewicka, Marta (Univ. of Pittsburgh, USA)

Lindgren, Erik (Uppsala University, Sweden)

Manfredi, Juan J. (Univ. of Pittsburgh, USA)

Medina, María (Univ. Autónoma de Madrid, Spain)

Ochoa, Pablo (Univ. Nacional de Cuyo-CONICET, Argentina)

Pagnini, Gianni (Basque Center for Applied Mathematics, Spain)

Parviainen, Mikko (Univ. of Jyväskylä, Finland)

Płociniczak, Łukasz (Wrocław University of Science and Technology, Poland)

Stan, Diana (Univ. of Cantabria, Spain)

Vazquez, Juan Luis (Univ. Autónoma de Madrid, Spain)