Sbordone, Carlo On some integral inequalities and their applications to the calculus of variations. (English) Zbl 0678.49008 Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 5, 73-94 (1986). 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. Cited in 8 Documents 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 Keywords:quasiconformal mappings; harmonic analysis; weighted Sobolev embedding theorems; regularity; variational problems; homogenization; \(\Gamma\)- convergence × Cite Format Result Cite Review PDF