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January  2009, 11(1): 57-65. doi: 10.3934/dcdsb.2009.11.57

Comparison results without strict convexity

Arrigo Cellina 1, , Carlo Mariconda 2, and  Giulia Treu 2,

1. 

Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy
2. 

Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy, Italy

Received  January 2007 Revised  February 2008 Published  November 2008

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: comparison theorems, Strict convexity.
Mathematics Subject Classification: Primary: 49K20; Secondary: 49K30.
Citation: Arrigo Cellina, Carlo Mariconda, Giulia Treu. Comparison results without strict convexity. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 57-65. doi: 10.3934/dcdsb.2009.11.57
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