Stability of the Solutions of Nonlinear Weighted Elliptic Equations Without the Weighted Sobolev Spaces Framework

DOI: 10.68381/jca33039 ISSN: 0944-6532

Lucio Boccardo, Pasquale Imparato, Luigi Orsina

We prove some stability results on sequences of solutions of weighted elliptic equations such as

-{\rm div}(s(x)|\nabla u_n |^{p-2}\,\nabla u_n) = f_n(x)\,,

− d i v ( s ( x ) ∣ ∇ u n ∣ p − 2 ∇ u n ) = f n ( x ) ,

under some assumptions on the convergence of the sequence

\{f_n\}

{ f n }

(either weak or strong in some Lebesgue space). Here

s(x)

s ( x )

is a positive weight belonging to the Sobolev space

W^{1,p}(\Omega)

W 1 , p ( Ω )

.

Outline