IJPAM: Volume 51, No. 1 (2009)

QUALITATIVE PROPERTIES OF INTEGRO-EXTREMAL
MINIMIZERS OF NON-HOMOGENEOUS
SCALAR FUNCTIONALS

Sandro Zagatti
Department of Functional Analysis
International School for Advanced Studies - ISAS (SISSA)
Via Beirut 2/4, Grignano (TS), I-34014, ITALY
e-mail: zagatti@sissa.it


Abstract.We study the properties of the integro-extremal minimizers of functionals of the form

\begin{displaymath} \F(u) = \int_\O f(x,Du)\, dx, \quad u\in \vp+W_0^{1,p}(\O). \end{displaymath}

We give a well posedness result and discuss the viscosity properties associated to the solution of the minimum problem in the non convex case.

Received: January 18, 2009

AMS Subject Classification: 49J45, 49K40, 49L25

Key Words and Phrases: integro-extremal minimizers of functionals, viscosity properties, minimum problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 1