Steiner symmetrization and periodic solutions of boundary value problems
type: Item
instance of: scholarly article
title: Steiner symmetrization and periodic solutions of boundary value problems
zbMATH Open document ID: 0803.35007
DOI: 10.4171/ZAA/504
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1994-09-01T00:00:00Z
review text: Summary: Let \(f^* = f^*(x,y)\) denote the monotone decreasing rearrangement of a function \(f = f(x,y)\) with respect to \(y\). If \(-\Delta u = f\), \(-\Delta v = f^*\) in the domain \(\Omega = (0,1) \times (0,1)\) and \(\partial u/ \partial n = \partial v/ \partial n = 0\) on the boundary \(\partial \Omega\) of \(\Omega\), then \(\text{osc} u \leq \text{osc} v\), where the quantity osc \(w\) for a function \(w\) is defined as the difference \(\sup w - \inf w\). Similar results are proved for periodic solutions of some boundary value problems in cylindrical domains.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 627644
zbMATH Keywords: Steiner symmetrization
zbMATH Keywords: monotone decreasing rearrangement
author: Friedemann Brock
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 627644