22 citations · 67 across the 16 of their papers we have counts for
19 papers
Convergence rates of the fractional to the local Dirichlet problem
Leon Bungert, Félix del Teso
We prove non-asymptotic rates of convergence in the -norm for the solution of the fractional Dirichlet problem to the solution of the local Dirichlet problem…
Higher-order asymptotic expansions and finite difference schemes for the fractional -Laplacian
Félix del Teso, María Medina, Pablo Ochoa
We propose a new asymptotic expansion for the fractional -Laplacian with precise computations of the errors. Our approximation is shown to hold in the whole range $p\in(1,\infty…
A convergent finite difference-quadrature scheme for the porous medium equation with nonlocal pressure
Félix del Teso, Espen R. Jakobsen
We introduce and analyze a numerical approximation of the porous medium equation with fractional potential pressure introduced by Caffarelli and Vázquez: \[ \partial_t u = \nabla \…
Evolution Driven by the Infinity Fractional Laplacian
Félix del Teso, Jørgen Endal, Espen R. Jakobsen +1
We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland, Caffarelli and Figalli (2012) as the infinitesimal generator of a non-Brow…
Uniform tail estimates and -convergence for finite-difference approximations of nonlinear diffusion equations
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We obtain new equitightness and -convergence results for finite-difference approximations of generalized porous medium equations of the form $$ \partial…
On asymptotic expansions for the fractional infinity Laplacian
Félix del Teso, Jørgen Endal, Marta Lewicka
We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional -Laplacian for . This o…
Estimates on translations and Taylor expansions in fractional Sobolev spaces
Félix del Teso, David Gómez-Castro, Juan Luis Vázquez
In this paper we study how the (normalised) Gagliardo semi-norms control translations. In particular, we prove that $\| u(\cdot + y) - u \|_{L^p (\ma…
The one-phase fractional Stefan problem
Félix del Teso, Jørgen Endal, Juan Luis Vázquez
We study the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in . In terms of the enthalpy $…
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[φ(u)]=f(x,t)…
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}^{σ,μ}[φ(u)…
Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions
Nicole Cusimano, Félix del Teso, Luca Gerardo-Giorda +1
In this work, we propose novel discretizations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup form…
On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form These eq…
Existence of weak solutions for a general porous medium equation with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We study the general nonlinear diffusion equation that describes a flow through a porous medium which is driven by a nonlocal pressure.…
An extension problem related to inverse fractional operators
Félix del Teso
It is well known from the work of Caffarelli and Silvestre that the fractional Laplacian for can be obtained as a Dirichlet-to-Neumann map through…
Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem problem for the anomalous diffusion equation $\partial_tu-\mathc…
Transformations of Self-Similar Solutions for porous medium equations of fractional type
Diana Stan, Félix del Teso, Juan Luis Vázquez
We consider four different models of nonlinear diffusion equations involving fractional Laplacians and study the existence and properties of classes of self-similar solutions. Such…
Finite and infinite speed of propagation for porous medium equations with fractional pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We study a porous medium equation with fractional potential pressure: for , and .…
Finite difference method for a general fractional porous medium equation
Félix del Teso, Juan Luis Vázquez
We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[ \frac{\partial u}{\partial t}+(-Δ)^{σ/2} (u^m)=0 \] posed for $x\in \mathbb{R}…
Finite difference method for a fractional porous medium equation
Félix del Teso
We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[\frac{\partial u}{\partial t}+(-Δ)^{1/2} (u^m)=0.\] The problem is posed in $x\…