Solutions to the L^p Mixed Boundary Value Problem in C^1,1 Domains

Author

Laura D. Croyle, University of KentuckyFollow

Date Available

7-19-2016

Year of Publication

2016

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Mathematics

Advisor

Dr. Russell Brown

Abstract

We look at the mixed boundary value problem for elliptic operators in a bounded C^1,1(ℝⁿ) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the L^p mixed problem has a unique solution with the non-tangential maximal function of the gradient in L^p(∂Ω).

Digital Object Identifier (DOI)

http://dx.doi.org/10.13023/ETD.2016.297

Recommended Citation

Croyle, Laura D., "Solutions to the L^p Mixed Boundary Value Problem in C^1,1 Domains" (2016). Theses and Dissertations--Mathematics. 38.
https://uknowledge.uky.edu/math_etds/38