Steiner symmetric extremals in Pólya–Szegö-type inequalities
Copyright policy )Steiner symmetric extremals in Pólya–Szegö-type inequalities
The aim of the present paper is to analyse the cases of equality in Steiner symmetrization inequalities for Dirichlet-type integrals. The results of the authors yield the Steiner symmetry of PS-extremals in the class of Sobolev, and more generally, BV functions, for a large class of functionals. The crucial assumption is that the derivative of the relevant extremal, in the direction orthogonal to the hyperplane of symmetrization, vanishes at most in a set of Lebesgue measure zero.
Mathematics(all), rearrangements of functions, functions of bounded variation, Steiner symmetrizatio; Polya-Szego inequality; Sobolev spaces; functions of bounded variation, Inequalities for sums, series and integrals, Dirichlet integrals, Sobolev functions, Rearrangements of functions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Variational inequalities, Functions of bounded variation
Mathematics(all), rearrangements of functions, functions of bounded variation, Steiner symmetrizatio; Polya-Szego inequality; Sobolev spaces; functions of bounded variation, Inequalities for sums, series and integrals, Dirichlet integrals, Sobolev functions, Rearrangements of functions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Variational inequalities, Functions of bounded variation
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