On the existence of extremal functions in Sobolev embedding theorems with critical exponents

DOI10.1090/S1061-0022-06-00929-0zbMath1113.49010WikidataQ125359209 ScholiaQ125359209MaRDI QIDQ5485840

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Publication date: 4 September 2006

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

minimizerscritical exponent\(p\)-LaplacianSobolev inequalitySobolev-Poincaré inequalityHardy-Sobolev inequality

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (9)

Lyapunov-type inequalities for partial differential equations with \(p\)-Laplacian ⋮ Existence of solutions of a non-linear eigenvalue problem with a variable weight ⋮ Minimal potential results for Schrödinger equations with Neumann boundary conditions ⋮ Poincaré trace inequalities in \(BV({\mathbb {B}}^n)\) with non-standard normalization ⋮ Balls minimize trace constants in BV ⋮ On the compactness problem of extremal functions to sharp Riemannian \(L^p\)-Sobolev inequalities ⋮ The effect of a discontinuous weight for a critical Sobolev problem ⋮ A rearrangement based proof for the existence of extremal functions for the Sobolev-Poincaré inequality on \(B^n\) ⋮ Solvability of a critical semilinear problem with the spectral Neumann fractional Laplacian

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