Regularity results for nonlocal variational inequalities. (English) Zbl 0894.49004

The paper deals with variational inequalities with nonlocal constraints \[ \langle -Au,v-u\rangle \geq \langle f,v-u\rangle, \quad \forall v \in K,\tag{1} \]
\[ u \in K = \{v \in H_0^1 (\Omega): \int_{\Omega} j(v(x)) dx \leq \alpha\}, \] where \(f \in H^{-1}(\Omega)\), \(\alpha\) is a given positive constant, \(\Omega \subset {R}^n\) is a bounded domain, \(n \geq 2\). The authors prove \(W^{2,p}(\Omega)\) regularity results for (1), assuming that \(f \in L^p(\Omega)\). The results are obtained via approximation of the problem (1) by a penalized nonlinear problem.
Reviewer: E.Minchev (Sofia)


49J40 Variational inequalities
49N60 Regularity of solutions in optimal control