Existence and regularity of monotone solutions to a free boundary problem
Name
61207849-MIT.pdf
Description
Full printable version
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2.31 MB
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Checksum (MD5)
4fa787efe471fd678c0da86a10f96669
Author(s)
De Silva, Daniela
Advisor(s)
David Jerison.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
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..
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 71-72).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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