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arXiv · 2103.00743

Interpolative gap bounds for nonautonomous integrals

Cristiana De Filippis·Giuseppe Mingione
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Abstract

For nonautonomous, nonuniformly elliptic integrals with so-called $(p,q)$-growth conditions, we show a general interpolation property allowing to get basic higher integrability results for H\"older continuous minimizers under improved bounds for the gap $q/p$. For this we introduce a new method, based on approximating the original, local functional, with mixed local/nonlocal ones, and allowing for suitable estimates in fractional Sobolev spaces.

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Cristiana De Filippis, Giuseppe Mingione. 2021-03-01. Interpolative gap bounds for nonautonomous integrals. https://arxiv.org/abs/2103.00743

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