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Free boundary problems and global solutions in half spaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , 10 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 2005:06
Keyword [en]
Mathematics
Keyword [sv]
MATEMATIK
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-195ISBN: 91-7178-065-3 (print)OAI: oai:DiVA.org:kth-195DiVA: diva2:7866
Public defence
2005-05-20, Sal D3, Lindstedtsvägen 5, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100830. Tidigare titel: Free boundary regularity near the fixed boundary. Titel ändrad 20100830 i enlighet med den tryckta avhandlingen.Available from: 2005-05-16 Created: 2005-05-16 Last updated: 2010-08-30Bibliographically approved
List of papers
1. On the regularity of a free boundary near contact points with a fixed boundary
Open this publication in new window or tab >>On the regularity of a free boundary near contact points with a fixed boundary
2007 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 232, no 1, 285-302 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the regularity of a free boundary near contact points with a fixed boundary, with C boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly C 1 up to the fixed boundary. We will also construct some examples of irregular free boundaries.

Keyword
OBSTACLE PROBLEM
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-24243 (URN)10.1016/j.jde.2006.06.012 (DOI)000243310800010 ()
Note
QC 20100830Available from: 2010-08-30 Created: 2010-08-30 Last updated: 2017-12-12Bibliographically approved
2. Global solutions of the obstacle problem in half-spaces, and their impact on local stability
Open this publication in new window or tab >>Global solutions of the obstacle problem in half-spaces, and their impact on local stability
2005 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 23, no 3, 271-279 p.Article in journal (Refereed) Published
Abstract [en]

We show that there are an abundance of non-homogeneous global solutions to the obstacle problem, in the half-space, Delta u = X-{u > 0}, u >= 0 inR(+)(2), with a (fixed) homogeneous boundary condition u(0, x(2)) = lambda(2) (x(2)(+))(2) (0 < lambda < 1/root 2) As a consequence we obtain local instability of the free boundary under C-1,C-1 perturbation, of the Dirichlet data.

Keyword
free-boundary, regularity
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-14843 (URN)10.1007/s00526-004-0299-0 (DOI)000229907100002 ()2-s2.0-31144465979 (Scopus ID)
Note
QC 20100830Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
3. The free boundary near the fixed boundary for the heat equation
Open this publication in new window or tab >>The free boundary near the fixed boundary for the heat equation
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-24244 (URN)
Note
QC 20100830Available from: 2010-08-30 Created: 2010-08-30 Last updated: 2010-08-30Bibliographically approved
4. On the De Giorgi conjecture in half spaces
Open this publication in new window or tab >>On the De Giorgi conjecture in half spaces
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-24245 (URN)
Note
QC 20100830Available from: 2010-08-30 Created: 2010-08-30 Last updated: 2010-08-30Bibliographically approved

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Citation style
  • apa
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