Revista Matemática Iberoamericana
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Published online: 2016-10-03
Boundary Harnack estimates in slit domains and applications to thin free boundary problemsDaniela De Silva and Ovidiu Savin (1) Columbia University, New York, USA
(2) Columbia University, New York, United States
We provide a higher order boundary Harnack inequality for harmonic functions in slit domains. As a corollary we obtain the $C^\infty$ regularity of the free boundary in the Signorini problem near non-degenerate points.
Keywords: Boundary Harnack inequality, free boundary problems
De Silva Daniela, Savin Ovidiu: Boundary Harnack estimates in slit domains and applications to thin free boundary problems. Rev. Mat. Iberoam. 32 (2016), 891-912. doi: 10.4171/RMI/902