2026-09-20T12:45:55Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/311602022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
David Jerison.
De Silva, Daniela
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-02-02T18:54:05Z
2006-02-02T18:54:05Z
2005
2005
http://hdl.handle.net/1721.1/31160
61207849
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 71-72).
In the first part of this dissertation, we provide the first example of a singular energy minimizing free boundary. This singular solution occurs in dimension 7 and higher, and in fact it is conjectured that there are no singular minimizers in dimension lower than 7. Our example is the analogue of the 8-dimensional Simons cone in the theory of minimal surfaces. The minimality of the Simons cone is closely related to the existence of a complete minimal graph in dimension 9, which is not a hyperplane. The first step toward solving the analogous problem in the free boundary context, consists in developing a local existence and regularity theory for monotone solutions to a free boundary problem. This is the objective of the second part of our thesis. We also provide a partial result in the global context..
by Daniela De Silva.
Ph.D.
72 p.
2412035 bytes
2419274 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Existence and regularity of monotone solutions to a free boundary problem
Thesis
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