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arXiv · 2110.15874

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

Elvira Mascolo·Antonia Passarelli di Napoli
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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.

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Elvira Mascolo, Antonia Passarelli di Napoli. 2021-10-29. Higher differentiability for a class of problems under p,q subquadratic growth. https://arxiv.org/abs/2110.15874

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