Strong versus weak local minimizers for the perturbed Dirichlet functional

Taheri, Ali (2002) Strong versus weak local minimizers for the perturbed Dirichlet functional. Calculus of Variations and Partial Differential Equations, 15 (2). pp. 215-235. ISSN 0944-2669

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Abstract

Let Omega subset of R-n be a bounded domain and F : Omega x R-N --> R. In this paper we consider functionals of the form I(u) := fOmega(1/2\Du\(2) + F(x, u)) dx, where the admissible function u belongs to the Sobolev space of vector-valued functions W-1,W-2 (Omega; R-N) and is such that the integral on the right is well defined. We state and prove a sufficiency theorem for L-r local minimizers of I where 1 less than or equal to r less than or equal to infinity. The exponent r is shown to depend on the dimension n and the growth condition of F and an exact expression is presented for this dependence. We discuss some examples and applications of this theorem.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Ali Taheri
Date Deposited: 06 Feb 2012 18:31
Last Modified: 09 Jul 2012 10:59
URI: http://sro.sussex.ac.uk/id/eprint/16912
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