Regularity results for the best-Sobolev-constant function

DOI10.1007/s10231-014-0425-3zbMath1334.46029OpenAlexW2013465570MaRDI QIDQ495617

Grey Ercole

Publication date: 14 September 2015

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-014-0425-3

zbMATH Keywords

\(p\)-Laplacianbest-Sobolev-constant\ functionSobolev immersion

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (5)

Uniqueness of extremals for some sharp Poincaré-Sobolev constants ⋮ On the first exterior \(p\)-harmonic Steklov eigenvalue ⋮ Computing the best constant in the Sobolev inequality for a ball ⋮ Remarks on the behavior of the best Sobolev constants ⋮ Ground state solutions for a semilinear elliptic problem with critical-subcritical growth

Cites Work

• Absolute continuity of the best Sobolev constant
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Elliptic equations with nearly critical growth
• Regularity for a more general class of quasilinear equations
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• An elementary proof of the uniqueness of positive radial solutions of a quasilinear Dirichlet problem
• Real analyticity and non-degeneracy
• Symmetry results for functions yielding best constants in Sobolev-type inequalities.
• The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
• On a problem of Huang concerning best constants in Sobolev embeddings
• On the resonant Lane–Emden problem for the p-Laplacian
• Quasilinear elliptic equations with nearly critical growth
• Boundary regularity for solutions of degenerate elliptic equations
• On Limits Of Solutions Of Elliptic Problems With Nearly Critical Exponent
• A note on the asymptotic behavior of positive solutions for some elliptic equation
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