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

Goldstein G. R., Goldstein J. A., KÖMBE İ., Tellioğlu R.

Annali di Matematica Pura ed Applicata, cilt.201, sa.6, ss.2927-2942, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 201 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10231-022-01226-6
  • Dergi Adı: Annali di Matematica Pura ed Applicata
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2927-2942
  • Anahtar Kelimeler: Critical exponents, Robin boundary conditions, Hardy-Leray type inequalities, Nonexistence, Positive solutions
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

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.