Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth
Analysis of PDEs
2019-10-10 v1
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.
Keywords
Cite
@article{arxiv.1910.03689,
title = {Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth},
author = {Andrea Gentile},
journal= {arXiv preprint arXiv:1910.03689},
year = {2019}
}