The aim of this paper is to prove existence results for nonlinear elliptic equations whose the prototype is −div (|u|^(p−2)u )= g ϕ in a open subset Ω of R^n, , u = 0 on \partial Omega , where p ≥2, the function ϕ( x) = (2π)^ (n/2) exp (−|x|^2 /2) is the density of Gauss measure and g \in L^1 (log L)^(1/2) This condition on the function g is sharp in the class of Zygmund spaces.
Existence results for nonlinear elliptic equations related to Gauss measure in a limit case / DI BLASIO, Giuseppina; Feo, Filomena; Posteraro, MARIA ROSARIA. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 7:6(2008), pp. 1497-1506.
Existence results for nonlinear elliptic equations related to Gauss measure in a limit case
DI BLASIO, GIUSEPPINA;FEO, FILOMENA;POSTERARO, MARIA ROSARIA
2008
Abstract
The aim of this paper is to prove existence results for nonlinear elliptic equations whose the prototype is −div (|u|^(p−2)u )= g ϕ in a open subset Ω of R^n, , u = 0 on \partial Omega , where p ≥2, the function ϕ( x) = (2π)^ (n/2) exp (−|x|^2 /2) is the density of Gauss measure and g \in L^1 (log L)^(1/2) This condition on the function g is sharp in the class of Zygmund spaces.| File | Dimensione | Formato | |
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