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Extremals of functionals with competing symmetries. (English) Zbl 0705.46016

Summary: We present a new method of producing optimizing sequences for highly symmetric functionals. The sequences have good convergence properties built in. We apply the method in different settings to give elementary proofs of some classical inequalities - such as the Hardy-Littlewood- Sobolev and the logarithmic Sobolev inequality - in their sharp form.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
49J40 Variational inequalities
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