132 research outputs found
The higher order regularity Dirichlet problem for elliptic systems in the upper-half space
We identify a large class of constant (complex) coefficient, second order
elliptic systems for which the Dirichlet problem in the upper-half space with
data in -based Sobolev spaces, , of arbitrary smoothness
, is well-posed in the class of functions whose nontangential maximal
operator of their derivatives up to, and including, order is
-integrable. This class includes all scalar, complex coefficient elliptic
operators of second order, as well as the Lam\'e system of elasticity, among
others
Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains
We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and
Krein-type resolvent formulas for Schr\"odinger operators on bounded Lipschitz
domains in \bbR^n, . We also discuss the case of bounded
-domains, .Comment: 61 pages, typos corrected, new material adde
Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains
Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type [Delta]u-N(x, u) = F(x), equipped with Dirichlet and Neumann boundary conditions
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