Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations

Silvia Cingolani, Marco Degiovanni, Berardino Sciunzi

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

Abstract

We establish critical groups estimates for the weak solutions of − Δ_p u = f(x, u) in Ω and u = 0 on ∂Ω via Morse index, where Ω is a bounded domain, f ∈ C^1(Ω×R) and f(x, s) > 0 for all x ∈ Ω, s > 0 and f(x, s) = 0 for all x ∈ Ω, s ≤ 0. The proof relies on new uniform Sobolev inequalities for approximating problems. We also prove critical groups estimates when Ω is the ball or the annulus and f is a sign changing function.
Lingua originaleEnglish
pagine (da-a)N/A-N/A
RivistaJournal of Functional Analysis
Volume286
DOI
Stato di pubblicazionePubblicato - 2024

Keywords

  • p-Laplace equations, critical groups, regularity theory, Sobolev embeddings

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