## 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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