Calculus of Variations and Geometric Measure Theory

Q. H. Nguyen - J. L. Vazquez

Porous medium equation with nonlocal pressure in a bounded domain

created by nguyen on 03 May 2018


Accepted Paper

Inserted: 3 may 2018
Last Updated: 3 may 2018

Journal: COM.PDE
Year: 2018

ArXiv: 1708.00660 PDF


We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space domain. We prove existence of weak solutions and suitable a priori bounds and regularity estimates.