University of Sussex
Browse

File(s) not publicly available

Strong versus weak local minimizers for the perturbed Dirichlet functional

journal contribution
posted on 2023-06-07, 20:23 authored by Ali TaheriAli Taheri
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.

History

Publication status

  • Published

Journal

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

Publisher

Springer

Issue

2

Volume

15

Page range

215-235

Pages

21.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC