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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
