We consider minimization problems of the form \[ \min_{u\in \varphi +\Wuu(\Omega)}\int_\Omega [f(Du(x))-u(x)]\, dx \] where $\Omega\subseteq \R^N$ is a bounded convex open set, and the Borel function $f\colon \R^N \to [0, +\infty]$ is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of $\Omega$ and the zero level set of $f$, we prove that the viscosity solution of a related Hamilton--Jacobi equation provides a minimizer for the integral functional.
Geometric constraints on the domain for a class of minimum problems / Crasta, Graziano; Malusa, Annalisa. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 9:(2003), pp. 125-133. [10.1051/cocv:2003003]
Geometric constraints on the domain for a class of minimum problems
CRASTA, Graziano;MALUSA, ANNALISA
2003
Abstract
We consider minimization problems of the form \[ \min_{u\in \varphi +\Wuu(\Omega)}\int_\Omega [f(Du(x))-u(x)]\, dx \] where $\Omega\subseteq \R^N$ is a bounded convex open set, and the Borel function $f\colon \R^N \to [0, +\infty]$ is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of $\Omega$ and the zero level set of $f$, we prove that the viscosity solution of a related Hamilton--Jacobi equation provides a minimizer for the integral functional.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
