Symmetry of minimizers for some nonlocal variational problems

DOI10.1016/j.jfa.2007.10.004zbMath1128.49003OpenAlexW2065402838MaRDI QIDQ2469832

Orlando Lopes, Mihai Mariş

Publication date: 11 February 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2007.10.004

zbMATH Keywords

Davey-Stewartson equationsymmetry of minimizersfractional powers of Laplaciannonlocal functionalChoquard functionalminimization under constraints

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Existence theories for optimal control problems involving partial differential equations (49J20) Geometric theory, characteristics, transformations in context of PDEs (35A30) Variational methods for second-order elliptic equations (35J20) Optimality conditions for free problems in two or more independent variables (49K10)

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Cites Work

• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Symmetry properties in systems of semilinear elliptic equations
• Symmetry results for semilinear elliptic systems in the whole space
• Symmetry or not?
• A general rearrangement inequality à la Hardy-Littlewood
• Long-time dynamics of the Schrödinger-Poisson-Slater system
• On the existence, regularity and decay of solitary waves to a generalized Benjamin-Ono equation
• Radial symmetry of minimizers for some translation and rotation invariant functionals
• Minimax theorems
• Nonlocal variational problems arising in long wave propagatioN
• On the existence of standing waves for a davey–stewartson system
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Model equations for waves in stratified fluids
• The Cauchy problem for Davey-Stewartson systems
• Existence and evenness of solitary-wave solutions for an equation of short and long dispersive waves
• Solitary-Wave Solutions of the Benjamin Equation
• Stability and instability of some nonlinear dispersive solitary waves in higher dimension
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