Show simple item record

dc.contributor.advisorDavid S. Jerison.en_US
dc.contributor.authorRaynor, Sarah Groff, 1977-en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2005-10-14T20:01:39Z
dc.date.available2005-10-14T20:01:39Z
dc.date.copyright2003en_US
dc.date.issued2003en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/29353
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.en_US
dc.descriptionIncludes bibliographical references (p. 57-58).en_US
dc.description.abstractWe 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 ...en_US
dc.description.statementofresponsibilityby Sarah Groff Raynor.en_US
dc.format.extent58 p.en_US
dc.format.extent1454139 bytes
dc.format.extent1453948 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectMathematics.en_US
dc.titleRegularity of Neumann solutions to an elliptic free boundary problemen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.oclc52769087en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record