We consider local minimizers \( u:{\mathbb{R}^2} \supset \Omega \to {\mathbb{R}^M} \) of the variational integral
with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of ∇u and the differentiability of u in the classical sense. A Liouville type theorem is also established. Bibliography: 25 titles.
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Translated from Problems in Mathematical Analysis 56, April 2011, pp. 137–148.
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Fuchs, M. Two-dimensional variational problems with a wide range of anisotropy. J Math Sci 175, 375–389 (2011). https://doi.org/10.1007/s10958-011-0352-4
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DOI: https://doi.org/10.1007/s10958-011-0352-4