Strict rearrangement inequalities: Nonexpansivity and periodic Gagliardo seminorms
This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are Pólya-Szego type inequalities for these rearrangements. We also deal with the...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/449141 |
| Acceso en línea: | https://hdl.handle.net/2117/449141 https://dx.doi.org/10.1090/tran/9510 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Anàlisi funcional |
| Sumario: | This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are Pólya-Szego type inequalities for these rearrangements. We also deal with the cases of equality. Our method uses, among others, some classical nonexpansivity results for rearrangements for which we provide some slight improvements. Our proof is based on the ideas of Frank and Seiringer, [J. Funct. Anal. 255 (2008), pp. 3407–3430], where a new proof to deal with the cases of equality in the nonexpansivity theorem was given, albeit in a special case involving the rearrangement of only one function. |
|---|