The Proximity of Free Boundary to Wedges and Planes
Seminar Room 2, Newton Institute Gatehouse
AbstractThe talk is about the geometry of free boundary striking the centre of the half ball B_1^+ where a wedge like boundary data is prescribed near the origin. It will be seen that the effect of the wedge-like data dooms the asymptotic shape of the free boundary and the homogeneous global solutions turn out to have wedge-like free boundary too. A delicate analysis involving monotonicity formula techniques is employed to furnish the main results, which are from a joint paper with H. Shahgholian (to appear in the Transactions of the AMS).
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