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arXiv · 1910.03689

Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth

Andrea Gentile
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Abstract

We consider a class of integral functionals with convex integrand with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x variable belongs to a suitable Sobolev space W^{1;q}. We prove a result of higer differentiability for the minimizers. We also infer a result of Lipschitz regularity of minimizers if q > n, and a result of higher integrability for the gradient if q = n. The novelty here is that we deal with integrands satisfying subquadratic growth conditions with respect to gradient variable.

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Andrea Gentile. 2019-10-08. Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth. https://arxiv.org/abs/1910.03689

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