Date of Award
4-2016
Degree Type
Thesis
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Donatella Danielli
Committee Chair
Donatella Danielli
Committee Member 1
Daniel Phillips
Committee Member 2
Monica Torres
Committee Member 3
Aaron Yip
Abstract
In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal varies with a Hölder modulus of continuity. As a consequence, the viscosity solution is in fact a classical solution to the problem.
Recommended Citation
Backing, Thomas H., "Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients" (2016). Open Access Dissertations. 619.
https://docs.lib.purdue.edu/open_access_dissertations/619