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

Daniela De Silva; Ovidiu Savin

doi:10.4171/rmi/902

JournalsrmiVol. 32, No. 3pp. 891–912

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

Daniela De Silva
Columbia University, New York, USA
- zbMATH Open
Ovidiu Savin
Columbia University, New York, United States
- MathSciNet
- zbMATH Open

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Abstract

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.

Cite this article

Daniela De Silva, Ovidiu Savin, Boundary Harnack estimates in slit domains and applications to thin free boundary problems. Rev. Mat. Iberoam. 32 (2016), no. 3, pp. 891–912

DOI 10.4171/RMI/902