We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which governs blowing-up points and rates, observing that it reflects the strong nonlinear characteristic of the system. By using it, we also prove that a single blowing-up solution exists in general domains, and construct examples of contractible domains where multiple blowing-up solutions are allowed to exist. We believe that a variety of new ideas and arguments developed here will help to analyze blowing-up phenomena in related Hamiltonian-type systems.

Multiple blowing-up solutions to critical elliptic systems in bounded domains / Kim, S.; Pistoia, A.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 281:2(2021). [10.1016/j.jfa.2021.109023]

Multiple blowing-up solutions to critical elliptic systems in bounded domains

Pistoia A.
2021

Abstract

We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which governs blowing-up points and rates, observing that it reflects the strong nonlinear characteristic of the system. By using it, we also prove that a single blowing-up solution exists in general domains, and construct examples of contractible domains where multiple blowing-up solutions are allowed to exist. We believe that a variety of new ideas and arguments developed here will help to analyze blowing-up phenomena in related Hamiltonian-type systems.
2021
Brezis-Nirenberg problem; Critical hyperbola; Lane-Emden systems; Multiple blowing-up solution
01 Pubblicazione su rivista::01a Articolo in rivista
Multiple blowing-up solutions to critical elliptic systems in bounded domains / Kim, S.; Pistoia, A.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 281:2(2021). [10.1016/j.jfa.2021.109023]
File allegati a questo prodotto
File Dimensione Formato  
Kim_Multiple_2021.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 753.86 kB
Formato Adobe PDF
753.86 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1680271
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 7
social impact