Cocompactness and minimizers for inequalities of Hardy-Sobolev type involving \(N\)-Laplacian

DOI10.1007/s00030-010-0063-4zbMath1200.35139OpenAlexW2015647999MaRDI QIDQ1959337

Adimurthi, Kyril Tintarev, João Marcos Bezerra do Ó

Publication date: 6 October 2010

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-010-0063-4

zbMATH Keywords

weak convergenceTrudinger-Moser inequalityconcentration compactnessPalais-Smale sequencesglobal compactnessasymptotic orthogonalityelliptic problems in two dimensions

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62)

Related Items (16)

Concentration-compactness and extremal problems for a weighted Trudinger–Moser inequality ⋮ Some sharp inequalities related to Trudinger-Moser inequality ⋮ On the planar Kirchhoff-type problem involving supercritical exponential growth ⋮ A subset of Caffarelli-Kohn-Nirenberg inequalities in the hyperbolic space \(\mathbb {H}^N\) ⋮ Extremals for a Hardy-Trudinger-Moser inequality with remainder terms ⋮ Singular supercritical Trudinger-Moser inequalities and the existence of extremals ⋮ An improvement for the Trudinger-Moser inequality and applications ⋮ Sobolev spaces of symmetric functions and applications ⋮ Concentration profiles for the Trudinger-Moser functional are shaped like toy pyramids ⋮ Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality ⋮ Compactness properties of critical nonlinearities and nonlinear Schrödinger equations ⋮ Trudinger-Moser type inequalities with vanishing weights in the unit ball ⋮ On a version of Trudinger-Moser inequality with Möbius shift invariance ⋮ Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero ⋮ Attainability of the best Sobolev constant in a ball ⋮ An improved Hardy-Trudinger-Moser inequality

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• Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator

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