Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1066.49003
Crasta, Graziano; Malusa, Annalisa
Geometric constraints on the domain for a class of minimum problems. (English)
[J] ESAIM, Control Optim. Calc. Var. 9, 125-133 (2003). ISSN 1292-8119; ISSN 1262-3377/e

Summary: We consider minimization problems of the form $$\min_{u\in \varphi +W^{1,1}_0 (\Omega )}\int_\Omega [f(Du(x))-u(x)]\,dx$$ where $\Omega \subseteq \Bbb R^N$ is a bounded convex open set, and the Borel function $f\colon \Bbb R^N \to [0, +\infty ]$ 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.

MSC 2000:: *49J10 Free problems in several independent variables (existence)
49L25 Viscosity solutions

Keywords: integral functional; existence; non-convex problems; non-coercive problems; viscosity solutions

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]