In the present paper we prove existence results for a class of nonlinear elliptic equations whose prototype is -div (|D u|^(p−2) Du ϕ( x) ) + |D u|^σ ϕ( x)= g ϕ ; where Ω is an open set, u=0 on \partial Ω; the function ϕ( x) = (2π)^ (n/2) exp (−|x|2 /2) is the density of Gauss measure and g \in the weighted Lorentz-Zygmund space L^r (log L)^(-1/2) (ϕ,Ω), 1<r<p’. The results are sharp in this class of spaces.
Existence results for a class of degenerate elliptic equations / Posteraro, MARIA ROSARIA; DI BLASIO, Giuseppina; Feo, Filomena. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 21:3-4(2008), pp. 387-400.
Existence results for a class of degenerate elliptic equations
POSTERARO, MARIA ROSARIA;DI BLASIO, GIUSEPPINA;FEO, FILOMENA
2008
Abstract
In the present paper we prove existence results for a class of nonlinear elliptic equations whose prototype is -div (|D u|^(p−2) Du ϕ( x) ) + |D u|^σ ϕ( x)= g ϕ ; where Ω is an open set, u=0 on \partial Ω; the function ϕ( x) = (2π)^ (n/2) exp (−|x|2 /2) is the density of Gauss measure and g \in the weighted Lorentz-Zygmund space L^r (log L)^(-1/2) (ϕ,Ω), 1| File | Dimensione | Formato | |
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