ON THE HARDY–POINCARÉ INEQUALITY WITH BOUNDARY SINGULARITIES

DOI10.1142/S0219199712500198zbMath1259.35077arXiv1008.4785OpenAlexW2029342685MaRDI QIDQ2905290

Mouhamed Moustapha Fall

Publication date: 27 August 2012

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.4785

zbMATH Keywords

existencenon-existenceextremalsHardy inequality

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational methods for second-order elliptic equations (35J20) Singular elliptic equations (35J75) Boundary value problems for second-order elliptic systems (35J57)

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Cites Work

• A note on Hardy's inequalities with boundary singularities
• The effect of curvature on the best constant in the Hardy-Sobolev inequalities
• Minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary
• Hardy-Sobolev critical elliptic equations with boundary singularities
• Extremal functions for Hardy's inequality with weight
• Dirichlet and Neumann problems to critical Emden-Fowler type equations
• On a class of two-dimensional singular elliptic problems
• Hardy-Sobolev Inequalities in a Cone
• Existence of minimizers for Schroedinger operators under domain perturbations with application to Hard's inequality