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Type: Artigo de periódico
Title: Existence and Symmetries for Elliptic Equations with Multipolar Potentials and Polyharmonic Operators
Author: Ferreira, LCF
Mesquita, CAAS
Abstract: This article concerns the existence and qualitative properties of solutions for semilinear elliptic equations with critical multipolar potentials and polyharmonic operators. The results are also new for the Laplacian case. They cover a large class of anisotropic potentials, and show that solutions are stable with respect to potential angular components. The analysis is performed H-k,(alpha) over bar -spaces which are a sum of weighted. L-infinity-spaces and seem to be a minimal framework for the potential profile of interest. For this purpose, a theory with basic properties for H-k,(alpha) over bar is developed, including optimal (and positive) decompositions, Holder-type inequality, and quasi-monotonicity of the norm. We investigate a concept of symmetry for solutions which extends radial symmetry and carries out an idea of invariance around singularities. Our approach can be employed in a number of other situations like exterior domains and other types of PDEs.
Subject: Elliptic equations
polyharmonic operator
multipolar potentials
existence of solutions
Country: EUA
Editor: Indiana Univ Math Journal
Citation: Indiana University Mathematics Journal. Indiana Univ Math Journal, v. 62, n. 6, n. 1955, n. 1982, 2013.
Rights: aberto
Date Issue: 2013
Appears in Collections:Unicamp - Artigos e Outros Documentos

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