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 Hölder 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 functionals, and allowing for suitable estimates in fractional Sobolev spaces.

Interpolative gap bounds for nonautonomous integrals / De Filippis, C.; Mingione, G.. - In: ANALYSIS AND MATHEMATICAL PHYSICS. - ISSN 1664-2368. - 11:3(2021). [10.1007/s13324-021-00534-z]

Interpolative gap bounds for nonautonomous integrals

De Filippis C.;Mingione G.
2021-01-01

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 Hölder 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 functionals, and allowing for suitable estimates in fractional Sobolev spaces.
2021
Interpolative gap bounds for nonautonomous integrals / De Filippis, C.; Mingione, G.. - In: ANALYSIS AND MATHEMATICAL PHYSICS. - ISSN 1664-2368. - 11:3(2021). [10.1007/s13324-021-00534-z]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2895059
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