Study of nonlinear elliptic problems of fourth order with critical exponents on compact Riemannian manifolds
type: Item
instance of: scholarly article
title: Study of nonlinear elliptic problems of fourth order with critical exponents on compact Riemannian manifolds
zbMATH Open document ID: 1050.58016
DOI: 10.1016/S0021-7824(03)00068-0
author: Daniela Caraffa
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2004-05-27T00:00:00Z
review text: The author, using variational methods, proves existence theorems of solutions for the following elliptic partial differential equation of fourth-order with critical Sobolev exponent on a compact Riemannian manifold \(M\) of dimension \(n\) larger than \(4:\) \[ \triangle^2 \varphi + \nabla \left[a(x)\nabla \varphi\right ] + h(x) \varphi =\lambda f(x)\varphi | \varphi| ^{N-2} \] where \(a(x), h(x), f(x)\) are smooth functions on \(M,\) \(f(x)\) is positive and \(N=2n/(n -4).\) The author also proves a related result for a compact Riemannian manifold with boundary of dimension \(n >4\).
reviewed by: Ricardo Sa Earp
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 35J35
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 2066882
zbMATH Keywords: elliptic partial differential equations
zbMATH Keywords: nonlinear elliptic problems
zbMATH Keywords: nonlinear critical problems
zbMATH Keywords: fourth order
zbMATH Keywords: compact Riemannian manifolds
zbMATH Keywords: critical Sobolev exponent.
MaRDI profile type: Publication
cites work: Problèmes isoperimetriques et espaces de Sobolev
cites work: Q4398855
cites work: Elliptic equations of fourth-order with critical exponents on compact Riemannian manifolds
cites work: Q4852325
cites work: Q3275400
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description: scientific article; zbMATH DE number 2066882