We continue and completely set up the spectral theory initiated in Castorina et al. [D. Castorina, P. Esposito, B. Sciunzi, Degenerate elliptic equations with singular nonlinearities, Calc. Var. Partial Differential Equations, 34 (2009), 279–306] for the linearized operator arising from Δ_p u+f(u)=0. We establish existence and variational characterization of all the eigenvalues, and by a weak Harnack inequality we deduce Hölder continuity for the corresponding eigenfunctions, this regularity being sharp. The Morse index of a positive solution can be now defined in the classical way, and we will illustrate some qualitative consequences one should expect to deduce from such information. In particular, we show that zero Morse index (or more generally, nondegenerate) solutions on the annulus are radial.

Castorina, D., Esposito, P., Sciunzi, B. (2011). Spectral theory for linearized p-Laplace equations. NONLINEAR ANALYSIS, 74(11), 3606-3613 [10.1016/j.na.2011.03.009].

Spectral theory for linearized p-Laplace equations

ESPOSITO, PIERPAOLO;
2011-01-01

Abstract

We continue and completely set up the spectral theory initiated in Castorina et al. [D. Castorina, P. Esposito, B. Sciunzi, Degenerate elliptic equations with singular nonlinearities, Calc. Var. Partial Differential Equations, 34 (2009), 279–306] for the linearized operator arising from Δ_p u+f(u)=0. We establish existence and variational characterization of all the eigenvalues, and by a weak Harnack inequality we deduce Hölder continuity for the corresponding eigenfunctions, this regularity being sharp. The Morse index of a positive solution can be now defined in the classical way, and we will illustrate some qualitative consequences one should expect to deduce from such information. In particular, we show that zero Morse index (or more generally, nondegenerate) solutions on the annulus are radial.
2011
Castorina, D., Esposito, P., Sciunzi, B. (2011). Spectral theory for linearized p-Laplace equations. NONLINEAR ANALYSIS, 74(11), 3606-3613 [10.1016/j.na.2011.03.009].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11590/152694
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 11
social impact