Abstract
We establish conditions for the convergence of minimizers and minimum values of integral and more general functionals on sets of functions defined by bilateral constraints in variable domains. The constraints and domains under consideration depend on the same natural parameter, and the constraints belong to Sobolev spaces related to the given domains. The main condition on the constraints is the convergence to zero of the measure of the set where the difference between the upper and lower constraints is less than a positive measurable function.
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