Regularity for the nonlinear Signorini problem |
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| Authors: | Emmanouil Milakis |
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| Institution: | a University of Washington, Department of Mathematics, PO Box 354350, Seattle, WA 98195, USA
b Courant Institute of Mathematical Sciences, New York University, 251 Mercer street, New York, NY 10012, USA |
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| Abstract: | We study the regularity of the solution to a fully nonlinear version of the thin obstacle problem. In particular we prove that the solution is C1,α for some small α>0. This extends a result of Luis Caffarelli of 1979. Our proof relies on new estimates up to the boundary for fully nonlinear equations with Neumann boundary data, developed recently by the authors. |
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| Keywords: | Signorini problem Thin obstacle problem Fully nonlinear elliptic equations Free boundary problems |
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