187 citations · 856 across the 36 of their papers we have counts for
4 papers · 1 filter
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains
Matteo Bonforte, Alessio Figalli, Juan Luis Vazquez
This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form , , wher…
Flatness implies smoothness for solutions of the porous medium equation
Clemens Kienzler, Herbert Koch, Juan Luis Vazquez
One of the major problems in the theory of the porous medium equation is the regularity of the solutions and the free boundaries. Here we assume flatness of the solution in space t…
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.…
Optimal Existence and Uniqueness Theory for the Fractional Heat Equation
Matteo Bonforte, Yannick Sire, Juan Luis Vazquez
We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation , , posed in the whole space $\mathbb{R…