Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian

Details Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian

2011-01-13

arxiv.org/abs/1101.2601v1

Mathematics

Analysis of PDEs

Scientific paper

We discuss the optimal regularity and nondegeneracy of a free boundary
problem related to the fractional Laplacian. This work is related to, but
addresses a different problem from, recent work of Caffarelli, Roquejoffre, and
Sire. A variant of the boundary Harnack inequality is also proved, where it is
no longer required that the function be 0 along the boundary.

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