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The Proximity of Free Boundary to Wedges and Planes

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Free Boundary Problems and Related Topics

The 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 ).

This talk is part of the Isaac Newton Institute Seminar Series series.

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