Calculus of Variations and Geometric Measure Theory

L. Lussardi - E. Mascolo

A uniqueness result for a class of non strictly convex variational problems

created by lussardi on 24 May 2016
modified on 25 Oct 2016


Published Paper

Inserted: 24 may 2016
Last Updated: 25 oct 2016

Journal: J. Math. Anal. Appl.
Volume: 446
Number: 2
Pages: 1687-1694
Year: 2017


Let $\Omega$ be a smooth domain in $\mathbb R^2$, we prove that if $g \colon [0,+\infty) \to [0,+\infty]$ is convex with $g(0) < g(t)$ whenever $t > 0$ then there exists an unique minimizer $u \in C^{0,1} (\Omega)$ of the functional $u \mapsto \int _{\Omega} g(
\nabla u
) \,dxdy$ among all Lipschitz-continuous functions that assume the same value of $u$ on $\partial \Omega$.