We prove a comparison principle for positive supersolutions and subsolutions to the Lane–Emden equation for the p-Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no regularity assumptions, both on the set and the functions. We then show that such a comparison principle can be applied to prove: uniqueness of solutions; sharp pointwise estimates for positive solutions in convex sets; localization estimates for maximum points and sharp geometric estimates for generalized principal frequencies in convex sets.

A comparison principle for the Lane–Emden equation and applications to geometric estimates

Brasco L.
Co-primo
;
Prinari F.
Co-primo
;
2022

Abstract

We prove a comparison principle for positive supersolutions and subsolutions to the Lane–Emden equation for the p-Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no regularity assumptions, both on the set and the functions. We then show that such a comparison principle can be applied to prove: uniqueness of solutions; sharp pointwise estimates for positive solutions in convex sets; localization estimates for maximum points and sharp geometric estimates for generalized principal frequencies in convex sets.
2022
Brasco, L.; Prinari, F.; Zagati, A. C.
File in questo prodotto:
File Dimensione Formato  
braprizag_final_rev.pdf

accesso aperto

Descrizione: Pre-print
Tipologia: Pre-print
Licenza: Creative commons
Dimensione 510.1 kB
Formato Adobe PDF
510.1 kB Adobe PDF Visualizza/Apri
1-s2.0-S0362546X22000451-main.pdf

solo gestori archivio

Descrizione: Full text editoriale
Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 901.08 kB
Formato Adobe PDF
901.08 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/11392/2488946
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact