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Journal of Convex Analysis 19 (2012), No. 3, 795--813
Copyright Heldermann Verlag 2012

Existence Results for a Non Coercive Homogeneous Nonlinear Elliptic Equation

Carlo Mariconda
Dipartimento di Matematica, Universitą degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy


\newcommand{\R}{\mathbb{R}} Let $a:\R^n\to\R^n$ be monotonic, but unnecessarily strictly monotonic. We study the existence of Lipschitz or locally Lipschitz solutions to the equation div$\,a(\nabla u) = 0$ when the Lipschitz boundary datum fulfills some recent unilateral Bounded Slope Conditions.

Keywords: Lipschitz, nonlinear, degenerate, elliptic, pde, convex.

MSC: 35J70, 35J15, 49K20

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