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- W1976209968 abstract "Let Ω⊂RN be a bounded C2 domain and Lκ=−Δ−κd2 where d=dist(.,∂Ω) and 0<κ≤14. Let α±=1±1−4κ, λκ the first eigenvalue of Lκ with corresponding positive eigenfunction ϕκ. If g is a continuous nondecreasing function satisfying ∫1∞(g(s)+|g(−s)|)s−22N−2+α+2N−4+α+ds<∞, then for any Radon measures ν∈Mϕκ(Ω) and μ∈M(∂Ω) there exists a unique weak solution to problem Pν,μ: Lκu+g(u)=ν in Ω, u=μ on ∂Ω. If g(r)=|r|q−1u (q>1), we prove that, in the supercritical range of q, a necessary and sufficient condition for solving P0,μ with μ>0 is that μ is absolutely continuous with respect to the capacity associated with the space B2−2+α+2q′,q′(RN−1). We also characterize the boundary removable sets in terms of this capacity. In the subcritical range of q we classify the isolated singularities of positive solutions. Soient Ω⊂RN un domaine de classe C2 et Lκ=−Δ−κd2 où d=dist(.,∂Ω) et 0<κ≤14. Soient α±=1±1−4κy,λκ la première valeur propre de Lκ et ϕκ la fonction propre positive correspondante. Si g est une fonction continue croissante vérifiant ∫1∞(g(s)+|g(−s)|)s−22N−2+α+2N−4+α+ds<∞, alors pour toutes mesures de Radon ν∈Mϕκ(Ω) et μ∈M(∂Ω), il existe une unique solution faible au problème Pν,μ : Lκu+g(u)=ν dans Ω, u=μ sur ∂Ω. Si g(r)=|r|q−1u (q>1), nous démontrons qu'une condition nécessaire et suffisante pour résoudre P0,μ avec μ>0 est que μ soit absolument continue par rapport à la capacité associée à l'espace B2−2+α+2q′,q′(RN−1). Cette capacité caractérise les ensembles éliminables du bord. Dans le cas sous-critique, nous classifions les singularités isolées au bord des solutions positives." @default.
- W1976209968 created "2016-06-24" @default.
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- W1976209968 date "2015-04-01" @default.
- W1976209968 modified "2023-09-25" @default.
- W1976209968 title "Measure boundary value problems for semilinear elliptic equations with critical Hardy potentials" @default.
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- W1976209968 doi "https://doi.org/10.1016/j.crma.2015.01.011" @default.
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