Published Paper
AI statement: 🟢 AI-Free: no AI used.

Inserted: 11 nov 2026
Last Updated: 11 nov 2026

Journal: J. Convex Anal.
Year: 2027
Doi: 10.68381/jca34001

Abstract:

We study the stability of solutions to a class of variational inequalities posed on obstacle-type convex sets, under Mosco-convergence. More precisely, for a fixed obstacle $\psi\in W_0^{1,p}(\Omega)\cap L^\infty(\Omega)$, we consider $u\in W_0^{1,p}(\Omega)\cap L^\infty(\Omega)$ satisfying $u\geq\psi$ a.e. and $\langle A(u),v-u\rangle+\int_{\Omega} H(x,u,\nabla u)(v-u)\geq 0$ for all $v\in W_0^{1,p}(\Omega)\cap L^\infty(\Omega)$ with $v\geq\psi$. Here, $A$ is a Leray-Lions type operator, mapping $W_0^{1,p}(\Omega)$ into its dual $W^{-1,p'}(\Omega)$, while $H(x,u,\nabla u)$ grows like $\vert\nabla u\vert^{p}$. Our main result establishes that the solutions are stable under Mosco-convergence of the constraint sets. This extends classical stability results to natural growth problems.