Abstract

Given a bounded open subset of RN\R^N, we study the convergence of a sequence (Kn)n∈N(\K_n)_{n\in\N} of closed convex subsets of W01,p(Ω)\wump (p∈]1,∞[p\in]1,\infty[) with gradient constraint, to a convex set K\K, in the Mosco sense. A particular case of the problem studied is when Kn={v∈W01,p(Ω):Fn(x,∇v(x))≤gn(x) for a.e. x in Ω}\K_n=\{v\in \wump: F_n(x,\gd v(x))\le g_n(x)\text{ for a.e. $x$ in }\Omega\}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result

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Suggested citation

A. Azevedo, L. Santos. “Convergence of Convex Sets with Gradient Constraint.” Journal of Convex Analysis 11 (2004), No. 2, 285–301. https://doi.org/10.68381/jca11019

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Published by Heldermann Verlag, 2004. Rights now held by Banach Press LLC.