H-1 VERSUS C1 LOCAL MINIMIZERS

Authors
BREZIS H NIRENBERG L
Citation
H. Brezis et L. Nirenberg, H-1 VERSUS C1 LOCAL MINIMIZERS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 317(5), 1993, pp. 465-472
Citations number
16
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
317
Issue
5
Year of publication
1993
Pages
465 - 472
Database
ISI
SICI code
0764-4442(1993)317:5<465:HVCLM>2.0.ZU;2-U
Abstract
We consider functionals of the form PHI (u) = (1/2) integral-OMEGA\del u\2-integral-OMEGA F (x, u). Under suitable assumptions we prove that a local minimizer of PHI in the C1 topology must be a local minimizer in the H-1 topology. This result is especially useful when the corres ponding equation admits a sub and super solution.