Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year

2016

Author dc:creator

• Backing, Thomas H

Contributors dc:contributor

• Donatella Danielli
• Daniel Phillips
• Monica Torres
• Aaron Yip

• Pure sciences
• Applied sciences
• Bernoulli
• Free boundary problems
• Parabolic
• Applied Mathematics
• Mathematics

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/619

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-1724