Regularity of a free boundary at the infinity point
Lavi Karp, Henrik Shahgholian · Communications in Partial Differential Equations · 2000
Suppose there is a nonnegative function u and an open set , satisfying where . Under a certain thickness condition on Rn/Ω, we prove that the boundary of is a graph of a C1function in a neighborhood of the origin. As a by-product of the method of the proof, we also obtain the following result: Replace xωby fxωwith a certain assumptions on f. Then for any solution u which is asymptotically nonnegative at infinity, there holds