Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds
type: Item
instance of: scholarly article
title: Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds
zbMATH Open document ID: 1171.35045
author: Nicolas Saintier
published in: Calculus of Variations and Partial Differential Equations
publication date: 2009-05-06T00:00:00Z
review text: The author considers the asymptotic behaviour in Sobolev spaces of sequences of solutions for Paneitz-type equations \(\triangle^{2}_{g}u+k_{\alpha}\triangle_{g}u+h_{\alpha}u=f u^{\frac{2(n-1)}{n-k-4}-1},\) \(u>0\), \(u\) \(G\)-invariant on a compact Riemannian manifold \((M,g)\) which is invariant by a subgroup of the group of isometries of \((M,g)\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 5551262
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Paneitz-type equation
zbMATH Keywords: Reimannian manifold
Wikidata QID: Q115387600
reviewed by: Jiaqi Mo
MaRDI profile type: Publication
full work available at URL: s00526-008-0213-2
OpenAlex ID: W2036599653
cites work: Q5658847
cites work: Q4945131
cites work: Q4699358
cites work: Q4440503
cites work: Paneitz-type operators and applications
cites work: Critical exponents, critical dimensions and the biharmonic operator
cites work: Best constants in Sobolev inequalities on Riemannian manifolds in the presence of symmetries
cites work: Optimal constants in critical Sobolev inequalities on Riemannian manifolds in the presence of symmetries
cites work: Q4953998
cites work: Sharp Sobolev inequalities of second order
cites work: Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients
cites work: Sobolev spaces in the presence of symmetries
cites work: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
cites work: A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
cites work: The concentration-compactness principle in the calculus of variations. The limit case. I
cites work: Positive solutions for a fourth order equation invariant under isometries
cites work: Asymptotic estimates and blow-up theory for critical equations involving the \(p\)-Laplacian
cites work: Changing sign solutions of a conformally invariant fourth-order equation in the Euclidean space
cites work: Best constant in critical Sobolev inequalities of second-order in the presence of symmetries
cites work: Q4933737
DOI: 10.1007/S00526-008-0213-2
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description: scientific article; zbMATH DE number 5551262