Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem
نویسندگان
چکیده
منابع مشابه
Cross-shaped and Degenerate Singularities in an Unstable Elliptic Free Boundary Problem
We investigate singular and degenerate behavior of solutions of the unstable free boundary problem ∆u = −χ{u>0} . First, we construct a solution that is not of class C and whose free boundary consists of four arcs meeting in a cross-shaped singularity. This solution is completely unstable/repulsive from above and below which would make it hard to get by the usual methods, and even numerics is n...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2006
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.11.008