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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
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