Higher differentiability for a class of problems under p,q subquadratic growth

Elvira Mascolo; Antonia Passarelli di Napoli

Higher differentiability for a class of problems under p,q subquadratic growth

Analysis of PDEs 2021-11-09 v2

Authors: Elvira Mascolo , Antonia Passarelli di Napoli

Abstract

We study the higher differentiability for nonlinear elliptic equation in divergence form $\mathcal{A}(x,Du)=b(x)$ . The result covers the cases in which $\mathcal{A}(x, \xi)$ satisfies $p,q$ growth, with $1<p<2$ in $\xi$ and a Sobolev dependence of with respect to $x$ . By means of an a-priori estimate we ensure the $W^{2,p}_{\mathrm{loc}}(\Omega)$ -property for the solution of the boundary value problem.

Keywords

higher differentiability nonlinear elliptic equation divergence form p,q growth a-priori estimate sobolev dependence

Cite

@article{arxiv.2110.15874,
  title  = {Higher differentiability for a class of problems under p,q subquadratic growth},
  author = {Elvira Mascolo and Antonia Passarelli di Napoli},
  journal= {arXiv preprint arXiv:2110.15874},
  year   = {2021}
}

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