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Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle
Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle
Theses and Dissertations--Mathematics
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).