Nonlinear variational inequalities with bilateral constraints coinciding on a set of positive measure

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Аннотация

We consider variational inequalities with invertible operators   in divergence form and constraint set a.e. in  where  is a nonempty bounded open set in  , , and  are measurable functions. Under the assumptions that the operators  G-converge to an invertible operator ,  , and there exist functions  such that  a.e. in  and  we establish the weak convergence in  of the solutions  of the specified variational inequalities to the solution  of a similar variational inequality with the operator  and the constraint set  The fundamental difference between the considered case and the previously studied case, where  is that, in general, the functionals  do not converge to  even weakly in  and the energy integrals  do not converge to .

Авторлар туралы

A. Kovalevsky

Krasovskii Institute of Mathematics and Mechanics UB RAS; Ural Federal University

Хат алмасуға жауапты Автор.
Email: alexkvl71@mail.ru
Ресей, Yekaterinburg; Yekaterinburg

Әдебиет тізімі

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