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Obstacle Problems for Green Potentials and for Parabolic Quasiminima

Petersson, Catarina LU (2005) In Doctoral Theses in Mathematical Sciences
Abstract
The thesis consists of two parts.



In the first part pure potential theoretic methods are employed to study the obstacle problem connected with a uniformly elliptic second-order differential operator in divergence form. Regular points of the obstacles are characterized by the classical Wiener criterion.



The second part deals with a class of functions satisfying a certain integral inequality. A prototype for this function class is



the class of subsolutions (or, more generally) the class of sub-quasiminima, associated to a degenerate nonlinear parabolic differential operator and to a couple of irregular obstacles. A sufficient condition on the obstacles for regularity of a point is... (More)
The thesis consists of two parts.



In the first part pure potential theoretic methods are employed to study the obstacle problem connected with a uniformly elliptic second-order differential operator in divergence form. Regular points of the obstacles are characterized by the classical Wiener criterion.



The second part deals with a class of functions satisfying a certain integral inequality. A prototype for this function class is



the class of subsolutions (or, more generally) the class of sub-quasiminima, associated to a degenerate nonlinear parabolic differential operator and to a couple of irregular obstacles. A sufficient condition on the obstacles for regularity of a point is given. (Less)
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingen består av två delar. I den första delen används rent potentialteoretiska metoder för att studera hinderproblemet hörande till en likformigt elliptisk andra ordningens differentialoperator på divergensform. Reguljära punkter till hindren karakteriseras med det klassiska Wiener-kriteriet.



Andra delen behandlar en klass av funktioner som uppfyller en viss integralolikhet. En prototyp för denna funktionsklass är klassen av sublösningar eller, allmännare, klassen av subkvasiminima, hörande till en degenererad ickelinjär parabolisk differentialoperator och till ett par irreguljära hinder. Ett tillräckligt villkor på hindren för att en punkt ska vara reguljär ges.
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author
supervisor
opponent
  • Professor Lindqvist, Peter, NTNU, Trondheim
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Functions, differential equations, Funktioner, differentialekvationer, Matematik, degenerate parabolic operators, Mathematics, quasiminima, obstacle problems, Green potentials
in
Doctoral Theses in Mathematical Sciences
pages
95 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Matematikcentrum, MH:C Sölvegatan 18, Lund
defense date
2005-09-29 10:15:00
ISSN
1404-0034
ISBN
91-628-6565-X
language
English
LU publication?
yes
id
bb1dae2e-7350-48b9-8552-669b3c0e1040 (old id 545314)
date added to LUP
2016-04-01 16:25:27
date last changed
2025-04-04 13:59:56
@phdthesis{bb1dae2e-7350-48b9-8552-669b3c0e1040,
  abstract     = {{The thesis consists of two parts.<br/><br>
<br/><br>
In the first part pure potential theoretic methods are employed to study the obstacle problem connected with a uniformly elliptic second-order differential operator in divergence form. Regular points of the obstacles are characterized by the classical Wiener criterion.<br/><br>
<br/><br>
The second part deals with a class of functions satisfying a certain integral inequality. A prototype for this function class is<br/><br>
<br/><br>
the class of subsolutions (or, more generally) the class of sub-quasiminima, associated to a degenerate nonlinear parabolic differential operator and to a couple of irregular obstacles. A sufficient condition on the obstacles for regularity of a point is given.}},
  author       = {{Petersson, Catarina}},
  isbn         = {{91-628-6565-X}},
  issn         = {{1404-0034}},
  keywords     = {{Functions; differential equations; Funktioner; differentialekvationer; Matematik; degenerate parabolic operators; Mathematics; quasiminima; obstacle problems; Green potentials}},
  language     = {{eng}},
  publisher    = {{Centre for Mathematical Sciences, Lund University}},
  school       = {{Lund University}},
  series       = {{Doctoral Theses in Mathematical Sciences}},
  title        = {{Obstacle Problems for Green Potentials and for Parabolic Quasiminima}},
  year         = {{2005}},
}