Approximation of Solutions to the Mixed Dirichlet-Neumann Boundary Value Problem on Lipschitz Domains

Author

Morgan F. Schreffler, University of KentuckyFollow

Author ORCID Identifier

http://orcid.org/0000-0003-4712-2227

Date Available

4-28-2017

Year of Publication

2017

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Mathematics

Advisor

Dr. Russell Brown

Abstract

We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space H¹(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H¹(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.

Digital Object Identifier (DOI)

https://doi.org/10.13023/ETD.2017.189

Recommended Citation

Schreffler, Morgan F., "Approximation of Solutions to the Mixed Dirichlet-Neumann Boundary Value Problem on Lipschitz Domains" (2017). Theses and Dissertations--Mathematics. 47.
https://uknowledge.uky.edu/math_etds/47