We consider positive critical points of Caffarelli–Kohn–Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry result for positive solutions. The governing operator is a weighted p-Laplace operator, which we consider for a general p∈(1,d). For p=2, the symmetry breaking region for extremals of Caffarelli–Kohn–Nirenberg inequalities was completely characterized in Dolbeault et al. (2016). Our results extend this result to a general p and are optimal in some cases.

Ciraolo G., Corso R. (2022). Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities. NONLINEAR ANALYSIS, 216 [10.1016/j.na.2021.112683].

Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities

Corso R.
2022-03-01

Abstract

We consider positive critical points of Caffarelli–Kohn–Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry result for positive solutions. The governing operator is a weighted p-Laplace operator, which we consider for a general p∈(1,d). For p=2, the symmetry breaking region for extremals of Caffarelli–Kohn–Nirenberg inequalities was completely characterized in Dolbeault et al. (2016). Our results extend this result to a general p and are optimal in some cases.
mar-2022
Settore MAT/05 - Analisi Matematica
Ciraolo G., Corso R. (2022). Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities. NONLINEAR ANALYSIS, 216 [10.1016/j.na.2021.112683].
File in questo prodotto:
File Dimensione Formato  
Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities.pdf

Solo gestori archvio

Tipologia: Versione Editoriale
Dimensione 896.97 kB
Formato Adobe PDF
896.97 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/10447/529070
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact