2026-09-19T11:34:56Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/293532022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
David S. Jerison.
Raynor, Sarah Groff, 1977-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-10-14T20:01:39Z
2005-10-14T20:01:39Z
2003
2003
http://hdl.handle.net/1721.1/29353
52769087
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 57-58).
We examine the regularity properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , in a weak sense. We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. These results include up-to-the boundary gradient estimates on harmonic functions with Neumann boundary conditions on convex domains. The main result is that the minimizer u is Lipschitz continuous. The proof in dimension 2 is by means of conformal mapping as well as a simplified monotonicity formula. In higher dimensions, the proof is via a maximum principle estimate for ...
by Sarah Groff Raynor.
Ph.D.
58 p.
1454139 bytes
1453948 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Regularity of Neumann solutions to an elliptic free boundary problem
Thesis
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Publication
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