Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities

Goldstein G. R., Goldstein J. A., KÖMBE İ., Balekoğlu R. T.

AMS Special Session Celebrating M.M. Rao’s Many Mathematical Contributions as he Turns 90 Years Old, 2019, California, Amerika Birleşik Devletleri, 9 - 10 Kasım 2019, cilt.774, ss.55-70 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 774
  • Doi Numarası: 10.1090/conm/774/15568
  • Basıldığı Şehir: California
  • Basıldığı Ülke: Amerika Birleşik Devletleri
  • Sayfa Sayıları: ss.55-70
  • Anahtar Kelimeler: Critical exponents, Hardy-Leray inequalities, Robin boundary conditions, positive solutions, nonexistence
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

We are primarily concerned with the absence of positive solutions of the following problem, ⎧ ∂u ⎪⎨ ∂t=Δ(um ) + V (x)um + λuq in Ω × (0, T ), u(x, 0) = u0 (x) ≥ 0 in Ω, ⎪⎩ ∂u ∂ν=β(x)u on ∂Ω × (0, T ), where 0 < m < 1, V ∈ L1loc(Ω),β∈ L1loc(∂Ω), λ ∈ R, q > 0, Ω ⊂ RN is a bounded open subset of RN with smooth boundary ∂Ω, and∂u is the ∂ν outer normal derivative of u on ∂Ω. Moreover, we also present some new sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation of our interest.