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New Pólya–Szegö-type inequalities and an alternative approach to comparison results for PDE's

F. Brock, F. Chiacchio, A. Ferone, A. Mercaldo, Friedemann Brock

Advances in Mathematics, Volume: 336, Pages: 316 - 334

Swansea University Author: Friedemann Brock

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Abstract

We prove some Pólya–Szegö type inequalities which involve couples of functions and their rearrangements. The inequalities reduce to the classical Pólya–Szegö principle when the two functions coincide. As an application, we give a different proof of a comparison result for solutions to Dirichlet boun...

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Published in: Advances in Mathematics
ISSN: 00018708
Published: Elsevier 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa48737
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Abstract: We prove some Pólya–Szegö type inequalities which involve couples of functions and their rearrangements. The inequalities reduce to the classical Pólya–Szegö principle when the two functions coincide. As an application, we give a different proof of a comparison result for solutions to Dirichlet boundary value problems for Laplacian equations.
Keywords: Pólya–Szegö principle, Steiner symmetrization, elliptic equations, comparison results
College: Faculty of Science and Engineering
Start Page: 316
End Page: 334