Rearrangements and convexity of level sets in PDE
type: Item
instance of: scholarly article
title: Rearrangements and convexity of level sets in PDE
zbMATH Open document ID: 0593.35002
author: Bernd Kawohl
published in: Lecture Notes in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The first part of this work is a survey on rearrangement technique and its applications to partial differential equations and the calculus of variations. The author studies in detail the main types of rearrangements for functions of one and several variables and uses the general theory to prove convexity or symmetry properties of solutions of differential equations. The applications include the treatment of some free boundary problems such as the dam problem, the capacitary problem, the theory of jets and cavities. The second part of the book concerns the applications of the maximum principle to obtain the same type of results. The work contains several original contributions of the author and solves many interesting problems and conjectures on the shape of free boundary of elliptic variational inequalities.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 49R50
zbMATH DE Number: 3953325
zbMATH Keywords: rearrangement technique
zbMATH Keywords: free boundary problems
zbMATH Keywords: dam problem
zbMATH Keywords: capacitary problem
zbMATH Keywords: theory of jets and cavities
zbMATH Keywords: maximum principle
zbMATH Keywords: elliptic variational inequalities
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0075060
OpenAlex ID: W1535130726
DOI: 10.1007/BFB0075060
description: scientific article; zbMATH DE number 3953325