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Estimating the integral of a function in terms of a distribution function of its gradient. (English) Zbl 0476.49030

##### MSC:
 49Q20 Variational problems in a geometric measure-theoretic setting 26D10 Inequalities involving derivatives and differential and integral operators 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 49J10 Existence theories for free problems in two or more independent variables