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MiS Preprint

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

John Andersson and Georg Weiss


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.

MSC Codes:
35R35, 35K35

Related publications

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