Local Estimates for Minimizers of Some Convex Integral Functional of the Gradient and the Strong Maximum Principle

Abstract

We consider a class of convex integral functionals with lagrangeans depending only on the gradient and satisfying a generalized symmetry assumption, which includes as a particular case the rotational symmetry. Adapting the method by A. Cellina we obtain a kind of local estimates for minimizers in the respective variational problems, which is applied then to deduce some versions of the Strong Maximum Principle in the variational setting.

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Correspondence to Vladimir V. Goncharov.

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Work supported by: projecto POCI/MAT/56727/2004 and Financiamento Programático Especial do CIMA-UE (Centro de Investigação em Matemática e Aplicações da Universidade de Évora, Portugal) both of FCT (Fundação para Ciência e Tecnologia, Portugal).

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Goncharov, V.V., Santos, T.J. Local Estimates for Minimizers of Some Convex Integral Functional of the Gradient and the Strong Maximum Principle. Set-Valued Anal 19, 179–202 (2011). https://doi.org/10.1007/s11228-011-0176-x

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Keywords

  • Strong Maximum Principle
  • Comparison theorems
  • Convex variational problems
  • Minkowski functional

Mathematical Subject Classifications (2010)

  • 49J10
  • 49J53
  • 49N15