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The smoothness of solutions to nonlinear variational inequalities. (English) Zbl 0278.49011
Consider a variational inequality: \[ u\in K\quad\text{and}\quad \int_\Omega Au(v-u)\,dx\geq \int_\Omega f(v-u)\quad \forall v\in K \] where \(K=\{v: v\geq \psi \;\text{in}\;\Omega\;\text{and}\;v=0\;\text{on}\;\partial\Omega\}\) and \(Au=-\sum D_ja_j(Du)\), \(a_j\) is \(C^2\) and satisfies \(a(p)-a(q)\cdot p-q\geq \nu\,| p-q|^2\) uniformly on bounded sets. Under some conditions, it is proved that \(u\in C^{1,1}(\Omega)\) and that \(Au\) is of bounded variation.
Reviewer: H. Brézis

MSC:
49J40 Variational inequalities
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