Year of Publication

2016

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department/School/Program

Mathematics

First Advisor

Dr. Russell Brown

Abstract

We look at the mixed boundary value problem for elliptic operators in a bounded C1,1(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 Lp mixed problem has a unique solution with the non-tangential maximal function of the gradient in Lp(∂Ω).

Digital Object Identifier (DOI)

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

Included in

Analysis Commons

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