Nonexistence of positive solutions for nonlinear parabolic Robin problems and Hardy–Leray inequalities
Abstract
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.
Publication Title
Annali di Matematica Pura ed Applicata
Recommended Citation
Goldstein, G., Goldstein, J., Kömbe, I., & Tellioğlu, R. (2022). Nonexistence of positive solutions for nonlinear parabolic Robin problems and Hardy–Leray inequalities. Annali di Matematica Pura ed Applicata, 201 (6), 2927-2942. https://doi.org/10.1007/s10231-022-01226-6
