Calculus of Variations and Geometric Measure Theory

L. Brasco

Global $L^\infty$ gradient estimates for solutions to a certain degenerate elliptic equation

created by brasco on 22 May 2010
modified on 06 Sep 2010


Accepted Paper

Inserted: 22 may 2010
Last Updated: 6 sep 2010

Journal: Nonlinear Anal.
Pages: 21
Year: 2010


In view of applications to the study of regularity properties of minimizers for a continuous model of transportation, which is a kind of divergence-constrained optimization problem, we prove a global $L^\infty$ gradient estimate for solutions of an elliptic equation, whose ellipticity constants degenerate at every point where $
\nabla u
\leq \delta$, with $\delta>0$. The exposition is as self-contained as possible.

Keywords: Traffic congestion, Degenerate elliptic equations, Neumann boundary value problem, nonconvex variational problems