Competition reaction–absorption in some elliptic and parabolic problems related to the Caffarelli–Kohn–Nirenberg inequalities
- Abdellaoui, Boumediene
- Peral, Ireneo
DOIAbstract
AbstractWe consider the following elliptic problem:(1){−div(|x|−2γ∇u)+u|x|2(γ+1)=f(x,u),u⩾0 in Ω,u|∂Ω=0 and the corresponding parabolic version(2){ut−div(|x|−2γ∇u)+u|x|2(γ+1)=f(x,u),u⩾0 in Ω×(0,T),u(x,t)=0for (x,t)∈∂Ω×(0,T),u(x,0)=φ(x)if x∈Ω, Ω⊂RN is a smooth bounded domain with 0∈Ω and −∞<γ<N−22. We will consider in particular the critical case where f(x,u)=λuα|x|2(γ+1) and α⩾1. Conditions on γ, λ, α are given to obtain existence and nonexistence result
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