Accepted Paper
Inserted: 11 oct 2012
Last Updated: 16 apr 2013
Journal: J. Math. Pures Appl.
Year: 2012
Abstract:
We consider a family of elliptic equations introduced in the context of traffic congestion. They have the form $\nabla \cdot (\nabla \mathcal{F}(\nabla u)) = f$, where $\mathcal{F}$ is a convex function which vanishes inside some convex set and is elliptic outside. Under some natural assumptions on $\mathcal{F}$ and $f$, we prove that the function $\nabla \mathcal{F}(\nabla u)$ is continuous in any dimension, extending a previous result by Santambrogio and Vespri valid only in dimension $2$.
Keywords: regularity, Degenerate elliptic PDEs
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