Revista Matemática Iberoamericana


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Volume 32, Issue 3, 2016, pp. 891–912
DOI: 10.4171/RMI/902

Published online: 2016-10-03

Boundary Harnack estimates in slit domains and applications to thin free boundary problems

Daniela De Silva[1] and Ovidiu Savin[2]

(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. Iberoamericana 32 (2016), 891-912. doi: 10.4171/RMI/902