*Accepted Paper*

**Inserted:** 22 may 2010

**Last Updated:** 6 sep 2010

**Journal:** Nonlinear Anal.

**Pages:** 21

**Year:** 2010

**Abstract:**

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

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