Reverse Hardy-Littlewood-Sobolev inequalities
| Autor: | Franca Hoffmann, José A. Carrillo, Matias G. Delgadino, Rupert L. Frank, Jean Dolbeault |
|---|---|
| Přispěvatelé: | Department of Mathematics [Imperial College London], Imperial College London, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Mathematisches Institut, Ludwig-Maximilians Universität München, California Institute of Technology (CALTECH), Department of Computing and Mathematical sciences, ANR-17-CE40-0030,EFI,Entropie, flots, inégalités(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
concentration
Pure mathematics regularity General Mathematics 35A23 26D15 35K55 46E35 49J40 01 natural sciences Power law Sobolev inequality mean field equations Mathematics - Analysis of PDEs minimizer FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] nonlinear diffusion Uniqueness 0101 mathematics Mathematics symmetrization Applied Mathematics 010102 general mathematics nonlinear springs uniqueness free energy interpolation 010101 applied mathematics Range (mathematics) Kernel (algebra) Reverse Hardy-Littlewood-Sobolev inequalities measure valued solutions existence of optimal functions Mean field theory 35A23 26D15 35K55 46E35 49J40 Exponent Symmetrization Euler-Lagrange equations Analysis of PDEs (math.AP) |
| Zdroj: | Journal de Mathématiques Pures et Appliquées Journal de Mathématiques Pures et Appliquées, Elsevier, 2019, 132, pp.133-165. ⟨10.1016/j.matpur.2019.09.001⟩ |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2019.09.001⟩ |
| Popis: | This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and the properties of the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with free energy functionals and nonlinear diffusion equations involving mean field drifts. This paper is based on the merging of arXiv:1803.06151 and arXiv:1803.06232 |
| Databáze: | OpenAIRE |
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