An optimal limiting 2𝐷 Sobolev inequality

DOI10.1090/S0002-9939-09-10159-4zbMath1193.46017MaRDI QIDQ3552139

Andrei Biryuk

Publication date: 13 April 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

double logarithmic inequalitylimiting Sobolev embedding theorems

Mathematics Subject Classification ID

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) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (2)

Scattering for the two dimensional NLS with (full) exponential nonlinearity ⋮ Sharp constants in the Sobolev embedding theorem and a derivation of the Brezis-Gallouet interpolation inequality

Cites Work

• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Best constant in Sobolev inequality
• On critical cases of Sobolev's inequalities
• Double logarithmic inequality with a sharp constant
• On optimization problems with prescribed rearrangements
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Nonlinear Schrödinger evolution equations
• Logarithmic Sobolev Inequalities
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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