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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
119/2006

A Parabolic Free Boundary Problem with Bernoulli Type Condition on the Free Boundary

John Andersson and Georg Weiss

Abstract

We consider the regularity of the free boundary of the following problem $$ \Delta u -\frac{\partial u}{\partial t}=0 \quad \textrm{ in } \{ u>0 \}, $$ with the free boundary condition $|\nabla u|=1.$

In particular we show that flat free boundary points are have regular space normal.

Received:
Oct 26, 2006
Published:
Oct 26, 2006
MSC Codes:
35R35, 35K35

Related publications

inJournal
2009 Repository Open Access
John Andersson and Georg S. Weiss

A parabolic free boundary problem with Bernoulli type condition on the free boundary

In: Journal für die reine und angewandte Mathematik (Crelle's Journal), 627 (2009), pp. 213-235