Journal of Convex Analysis 33 (2026), No. 3&4, 629--635
Copyright Heldermann Verlag 2026
Stability of the Solutions of Nonlinear Weighted Elliptic Equations Without the Weighted Sobolev Spaces Framework
Lucio Boccardo
Istituto Lombardo, Sapienza Università, Roma, Italy
boccardo@mat.uniroma1.it
Pasquale Imparato
pasquale.imparato1994@gmail.com
Luigi Orsina
Dipartimento di Matematica, Sapienza Università, Roma, Italy
orsina@mat.uniroma1.it
[Abstract-pdf]
We prove some stability results on sequences of solutions of weighted elliptic equations such as $$ -{\rm div}(s(x)|\nabla u_n |^{p-2}\,\nabla u_n) = f_n(x)\,, $$ under some assumptions on the convergence of the sequence $\{f_n\}$ (either weak or strong in some Lebesgue space). Here $s(x)$ is a positive weight belonging to the Sobolev space $W^{1,p}(\Omega)$.
Keywords: Weighted elliptic equations, stability of solutions, weak and strong convergence.
MSC: 35J15, 35J60, 35J66.
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