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

  • Andrea Gentile EMAIL logo
Veröffentlicht/Copyright: 19. März 2020

Abstract

We consider functionals of the form

( v , Ω ) = Ω f ( x , D v ( x ) ) 𝑑 x ,

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 higher differentiability result for the minimizers. We also infer a Lipschitz regularity result 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.

MSC 2010: 49N60; 35J60; 49N99

Communicated by Frank Duzaar


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Received: 2019-10-23
Revised: 2019-12-27
Accepted: 2020-01-28
Published Online: 2020-03-19
Published in Print: 2022-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 26.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/acv-2019-0092/html
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