20 citations · 26 across the 4 of their papers we have counts for
8 papers
Boundedness and contractive estimates for orthotropic, widely degenerate, doubly nonlinear diffusion equations
Pasquale Ambrosio, Matias Vestberg
We study the regularity of weak solutions to doubly nonlinear orthotropic evolution equations of the form \[ \partial_{t}(\vert u\vert^{α-1}u)-\sum_{i=1}^{N}\partial_{i}\left[a_{i}…
Boundedness, Ultracontractive Bounds and Optimal Evolution of the Support for Doubly Nonlinear Anisotropic Diffusion
Simone Ciani, Vincenzo Vespri, Matias Vestberg
We investigate some regularity properties of a class of doubly nonlinear anisotropic evolution equations whose model case is \begin{align*} \partial_t \big(|u|^{α-1}u \big) - \sum^…
Tug-of-war with Kolmogorov
Carmina Fjellström, Kaj Nyström, Matias Vestberg
We introduce a new class of strongly degenerate nonlinear parabolic PDEs $(X,Y,t)\in\mathb…
Solving the Dirichlet problem for the Monge-Ampère equation using neural networks
Kaj Nyström, Matias Vestberg
The Monge-Ampère equation is a fully nonlinear partial differential equation (PDE) of fundamental importance in analysis, geometry and in the applied sciences. In this paper we sol…
Existence of Solutions to a Diffusive Shallow Medium Equation
Verena Bögelein, Nicolas Dietrich, Matias Vestberg
In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equa…
An extensive study of the regularity properties of solutions to doubly singular equations
Vincenzo Vespri, Matias Vestberg
In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfl…
Local Boundedness of Weak Solutions to the Diffusive Wave Approximation of the Shallow Water Equations
Thomas Singer, Matias Vestberg
In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations …
Crater functions for compound materials: a route to parameter estimation in coupled-PDE models of ion bombardment
Scott A. Norris, Juha Samela, Matias Vestberg +2
During the ion bombardment of targets containing multiple component species, highly-ordered arrays of nanostructures are sometimes observed. Models incorporating coupled partial di…