Optimal Sobolev type inequalities in Lorentz spaces

DOI10.1007/s11118-012-9329-2zbMath1288.46025OpenAlexW1964760962WikidataQ59278474 ScholiaQ59278474MaRDI QIDQ372811

Bernhard Ruf, Daniele Cassani, Cristina Tarsi

Publication date: 21 October 2013

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11383/1783717

zbMATH Keywords

elliptic equationscritical growthSobolev inequalitiesLorentz spacesbest constantsoptimal embeddings

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (17)

The Wolff potential estimate for solutions to elliptic equations with signed data ⋮ Wave equations with moving potentials ⋮ Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities ⋮ A note on the embedding theorems for Sobolev-Lorentz spaces ⋮ Optimality problems in Orlicz spaces ⋮ Cocompact embedding theorem for functions of bounded variation into Lorentz spaces ⋮ Fractional \(p\)-Laplacian problem with critical Stein-Weiss type term ⋮ Minimization problem associated with an improved Hardy-Sobolev type inequality ⋮ Some isoperimetric inequalities on \(\mathbb{R}^N\) with respect to weights \(|x|^{\alpha}\) ⋮ Sharp Sobolev inequalities in Lorentz spaces for a mean oscillation ⋮ The Dirichlet problem for singular elliptic equations with general nonlinearities ⋮ Bounds for best constants in subcritical Sobolev embeddings ⋮ Weak-type estimates and potential estimates for elliptic equations with drift terms ⋮ Equivalent and attained version of Hardy's inequality in \(\mathbb{R}^n\) ⋮ Maximal non-compactness of Sobolev embeddings ⋮ Bounds for subcritical best Sobolev constants in \(W^{1, p}\) ⋮ Attainability of the best Sobolev constant in a ball

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• On a version of Trudinger-Moser inequality with Möbius shift invariance
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