Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Russell Brown
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)
Croyle, Laura D., "Solutions to the Lp Mixed Boundary Value Problem in C1,1 Domains" (2016). Theses and Dissertations--Mathematics. 38.