Global summability for solutions to some anisotropic elliptic systems
type: Item
instance of: scholarly article
title: Global summability for solutions to some anisotropic elliptic systems
zbMATH Open document ID: 1344.35033
author: Francesco Leonetti
author: Pier Vincenzo Petricca
published in: Advances in Differential Equations
publication date: 2015-11-02T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ade/1439901073
review text: This paper is devoted to the study of the following anisotropic elliptic system of \(N\) partial differential equations \[ \begin{cases} \sum_{i=1}^n D_i(a_i^{\alpha}(x, Du(x)))=0,\quad & x\in \Omega,\\ u(x)=u_*(x),\quad & x\in \partial\Omega,\end{cases}\tag{1} \] where \(u: \Omega \rightarrow \mathbb R^N, \Omega \) is a bounded open subset of \(\mathbb R^n\) and \(a_i^{\alpha}: \Omega \times \mathbb R^{N\times n} \rightarrow \mathbb R\), \(1\leq \alpha \leq N\), with \( x \mapsto a_i^{\alpha} (x; z)\) measurable and \( z \mapsto a_i^{\alpha} (x; z)\) continuous. By assuming suitable ellipticity and growth conditions on \(a_i^{\alpha}\), the authors show that high degree of integrability of boundary datum \(u_*\) improves the integrability of the solution \(u\) of problem \((1)\). Moreover, with further Lipschitz continuity and monotonicity conditions, they improve the degree of integrability of the solution.
reviewed by: Said El Manouni
Mathematics Subject Classification ID: 35J58
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 6503087
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6503087