Asymptotics of best Sobolev constants on thin manifolds

DOI10.1016/j.jde.2008.10.022zbMath1244.53045OpenAlexW2006513647MaRDI QIDQ1014729

Nicolas Saintier

Publication date: 29 April 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.10.022

zbMATH Keywords

weighted Sobolev spacesasymptotic behaviourcompact manifold with boundarylimit manifold

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (1)

Fractional problems in thin domains

Cites Work

• The concentration-compactness principle in the calculus of variations. The limit case. II
• Estimates for the Sobolev trace constant with critical exponent and applications
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Best constants in Sobolev trace inequalities
• The behavior of the best Sobolev trace constant and extremals in thin domains.
• Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains.
• Asymptotic behaviour of sharp Sobolev constants in thin domains
• ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT
• The 𝐴𝐵 program in geometric analysis: sharp Sobolev inequalities and related problems
• Unnamed Item

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