Variational integrals with a wide range of anisotropy

Bildhauer, M.; Fuchs, M.; Zhong, X.

doi:10.1090/S1061-0022-07-00970-3

Variational integrals with a wide range of anisotropy
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by M. Bildhauer, M. Fuchs and X. Zhong

St. Petersburg Math. J. 18 (2007), 717-736

DOI: https://doi.org/10.1090/S1061-0022-07-00970-3

Published electronically: August 9, 2007

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Abstract:

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 $q\leq 2p$, and a famous counterexample of Giaquinta is discussed. In the vector case, some higher integrability result for the gradient is obtained.

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