Variational integrals with a~wide range of anisotropy

M. Bildhauer ; M. Fuchs ; X. Zhong

Algebra i analiz, Tome 18 (2006) no. 5, pp. 46-71.

Résumé

Anisotropic variational integrals of $(p,q)$-growth are considered. For the scalar case, the interior $C^{1,\alpha}$-regularity of bounded local minimizers is proved under the assumption that $q\le 2p$, and a famous counterexample of Giaquinta is discussed. In the vector case, some higher integrability result for the gradient is obtained.

Détail

Keywords: anisotropic problems, regularity of minimizers.

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