Comparison results without strict convexity

Arrigo Cellina; Carlo Mariconda; Giulia Treu

doi:10.3934/dcdsb.2009.11.57

Article Contents

2009, Volume 11, Issue 1: 57-65. Doi: 10.3934/dcdsb.2009.11.57

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Comparison results without strict convexity

1.
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano
2.
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste 63, 35121 Padova

Received: January 2007

Revised: February 2008

Published: July 2009

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we establish a comparison result for solutions to the problem

$\mbox{minimize}\int_\Omega l(||\nabla u(x)||)dx $

or to the problem

$\mbox{minimize}\int_\Omega l(\gamma_C(\nabla u(x))dx, $

for a special class of solutions, without assuming neither smoothness nor strict convexity of $l$.

Keywords:

Strict convexity,
comparison theorems.

Mathematics Subject Classification: Primary: 49K20; Secondary: 49K30.

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