Interior \(W^{2, p(x)}\)-regularity for elliptic equations of nondivergence form
type: Item
instance of: scholarly article
title: Interior \(W^{2, p(x)}\)-regularity for elliptic equations of nondivergence form
zbMATH Open document ID: 1330.35095
author: Xia Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-11-18T00:00:00Z
review text: The paper deals with second order uniformly elliptic equations of the form \[ \sum_{i,j=1}^n a^{ij}(x) \dfrac{\partial^2 u}{\partial x_i\partial x_j}=f\quad \text{a.e. in} \;\Omega\subset \mathbb{R}^n, \] where the principal coefficients belong to \(L^\infty_{\text{loc}}(\Omega)\cap VMO_{\text{loc}}(\Omega).\) Assuming log-Hölder continuity of \(p(\cdot),\) the author proves that \(f\in L^{p(x)}(\Omega)\) implies \(u\in W^{2,p(x)}_{\text{loc}}(\Omega)\) for the strong solutions.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6511580
zbMATH Keywords: second order elliptic equations
zbMATH Keywords: interior regularity
zbMATH Keywords: strong solution
zbMATH Keywords: nondivergence form
zbMATH Keywords: \(W^{2, p(x)}\)
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.10.017
OpenAlex ID: W2197325340
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DOI: 10.1016/J.JMAA.2015.10.017
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description: scientific article; zbMATH DE number 6511580