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

By D. Silva, Ovidiu Savin. 2014

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/98fe9c12a09e953edb393dc94220c3463ec8dadd