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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Backing, Thomas H"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Donatella Danielli","Daniel Phillips","Monica Torres","Aaron Yip"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-04-01T07:00:00Z","date_published":"2016-04-01T07:00:00Z","updated_at":"2026-07-24T03:53:47Z","subjects":["Pure sciences","Applied sciences","Bernoulli","Free boundary problems","Parabolic","Applied Mathematics","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/619","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Donatella Danielli","Daniel Phillips","Monica Torres","Aaron Yip"]},{"key":"dc:creator","label":"Author","values":["Backing, Thomas H"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Pure sciences","Applied sciences","Bernoulli","Free boundary problems","Parabolic","Applied Mathematics","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://docs.lib.purdue.edu/open_access_dissertations/619"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients"]}]}],"canonical_facts":{"dc:contributor":["Donatella Danielli","Daniel Phillips","Monica Torres","Aaron Yip"],"dc:creator":["Backing, Thomas H"],"dc:description.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.
"],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/619"],"dc:subject":["Pure sciences","Applied sciences","Bernoulli","Free boundary problems","Parabolic","Applied Mathematics","Mathematics"],"dc:title":["Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:53:47Z"}