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On some integral inequalities and their applications to the calculus of variations. (English) Zbl 0678.49008

We describe some integral inequalities that arise in various fields of analysis: 1. quasiconformal mappings, 2. harmonic analysis, 3. weighted Sobolev embedding theorems, 4. regularity of solutions of variational problems, 5. homogenization and \(\Gamma\)-convergence.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
26D10 Inequalities involving derivatives and differential and integral operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems