SYMMETRY BREAKING OF EXTREMAL FUNCTIONS FOR THE CAFFARELLI– KOHN–NIRENBERG INEQUALITIES

DOI10.1142/S0219199702000786zbMath1010.35029MaRDI QIDQ3153740

Jaeyoung Byeon, Zhi-Qiang Wang

Publication date: 26 November 2002

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

zbMATH Keywords

weighted Sobolev inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods for second-order elliptic equations (35J20) Inequalities involving derivatives and differential and integral operators (26D10)

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Cites Work

• Unnamed Item
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Best constant in Sobolev inequality
• On the existence of extremal functions for a weighted Sobolev embedding with critical exponent
• Singular minimization problems
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On the Best Constant for a Weighted Sobolev-Hardy Inequality
• Interpolation inequalities with weights