Nonexistence of positive solutions for nonlinear parabolic Robin problems and Hardy–Leray inequalities

Autor: Gisèle Ruiz Goldstein, Jerome A. Goldstein, Ismail Kömbe, Reyhan Tellioğlu
Přispěvatelé: Fakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümü
Rok vydání: 2022
Předmět:
Zdroj: Annali di Matematica Pura ed Applicata (1923 -). 201:2927-2942
ISSN: 1618-1891
0373-3114
Popis: The purpose of this paper is twofold. First is the study of the nonexistence of positive solutions of the parabolic problem {∂u∂t=Δpu+V(x)up-1+λuqinΩ×(0,T),u(x,0)=u0(x)≥0inΩ,|∇u|p-2∂u∂ν=β|u|p-2uon∂Ω×(0,T),where Ω is a bounded domain in RN with smooth boundary ∂Ω, Δpu= div (| ∇ u| p-2∇ u) is the p-Laplacian of u, V∈Lloc1(Ω), β∈Lloc1(∂Ω), λ∈ R, the exponents p and q satisfy 1 < p< 2 , and q> 0. Then, we present some sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation we are interested in.
Databáze: OpenAIRE
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