In this paper we study semilinear variational inequalities driven by an elliptic operator not in divergence form in a bounded domain with smooth boundary. Even if this problem is not variational in nature, we will prove the existence of non-trivial non-negative solutions for it, performing a variational approach combined with a penalization technique. This kind of approach seems to be new for problems of this type. We also prove a regularity result for the solutions of our problem.
On Variational Inequalities Driven by Elliptic Operators Not in Divergence Form
SERVADEI, RAFFAELLA
2012
Abstract
In this paper we study semilinear variational inequalities driven by an elliptic operator not in divergence form in a bounded domain with smooth boundary. Even if this problem is not variational in nature, we will prove the existence of non-trivial non-negative solutions for it, performing a variational approach combined with a penalization technique. This kind of approach seems to be new for problems of this type. We also prove a regularity result for the solutions of our problem.File in questo prodotto:
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