Asymptotics for the best Sobolev constants and their extremal functions

DOI10.1002/mana.201500263zbMath1355.35081arXiv1506.00922OpenAlexW2949836114MaRDI QIDQ2825992

Gilberto A. Pereira, Grey Ercole

Publication date: 14 October 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00922

zbMATH Keywords

asymptotic behaviorbest Sobolev constants\(p\)-LaplacianSobolev inequalitiesviscosity solutionsinfinity LaplacianDirac delta function

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Viscosity solutions to PDEs (35D40) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (16)

The limiting behavior of global minimizers in non-reflexive Orlicz-Sobolev spaces ⋮ On a singular minimizing problem ⋮ An optimal pointwise Morrey-Sobolev inequality ⋮ On a family of problems driven by rapidly growing operators ⋮ On the behavior of least energy solutions of a fractional ( p , q ( p ) )-Laplacian problem as p goes to infinity ⋮ Approximation of the least Rayleigh quotient for degree \(p\) homogeneous functionals ⋮ Computing the best constant in the Sobolev inequality for a ball ⋮ Asymptotic behavior of extremals for fractional Sobolev inequalities associated with singular problems ⋮ Remarks on the behavior of the best Sobolev constants ⋮ Asymptotic behaviour asp→ ∞ of least energy solutions of a (p, q(p))-Laplacian problem ⋮ The limiting behaviour of solutions to a family of eigenvalue problems ⋮ A limiting problem for a family of eigenvalue problems involving \(p\)-Laplacians ⋮ Extremal functions for Morrey's inequality in convex domains ⋮ The limiting behavior of constrained minimizers in Orlicz-Sobolev spaces ⋮ On the monotonicity of the best constant of Morrey’s inequality in convex domains ⋮ Minimization of quotients with variable exponents

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• Some properties of the ground states of the infinity Laplacian

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