Semilinear elliptic problems and concentration compactness on non-compact Riemannian man\-i\-folds

DOI10.1007/BF02930997zbMath1038.58024OpenAlexW2091570839WikidataQ115391072 ScholiaQ115391072MaRDI QIDQ1414833

Karl-Heinz Fieseler, Kyril Tintarev

Publication date: 4 December 2003

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02930997

zbMATH Keywords

Riemannian manifoldcritical pointsLaplace-Beltrami operatorsemilinear equationconcentration compactness

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20)

Related Items (9)

Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation ⋮ Cocompact embedding theorem for functions of bounded variation into Lorentz spaces ⋮ On the defect of compactness in Sobolev embeddings on Riemannian manifolds ⋮ Localized nodal solutions for system of critical Choquard equations ⋮ Compact embedding results of Sobolev spaces and existence of positive solutions to quasilinear equations ⋮ Concentration-compactness principle for nonlocal scalar field equations with critical growth ⋮ Subelliptic Sobolev spaces for manifolds with symmetries ⋮ On a version of Trudinger-Moser inequality with Möbius shift invariance ⋮ Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations

Cites Work

• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Symétrie et compacité dans les espaces de Sobolev
• Sobolev spaces in the presence of symmetries
• Sobolev spaces on Riemannian manifolds
• On the Grushin operator and hyperbolic symmetry
• On the elliptic equation Δ𝑢+𝑘𝑢-𝐾𝑢^{𝑝}=0 on complete Riemannian manifolds and their geometric applications
• A compactness lemma
• Mountain pass and impasse for nonsmooth functionals with constraints
• An abstract version of the concentration compactness principle.
• The Brézis-Nirenberg problem on \(\mathbb{S}^3\)

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