Inserted: 22 may 2010
Last Updated: 6 sep 2010
Journal: Nonlinear Anal.
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 $
\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