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Showing 1 to 3 of 3 for “"Sobolev regularity"”.
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Regularity of the Bergman Projection on Variants of the Hartogs Triangle
… its behavior on other function spaces, e.g. Lp, Sobolev and Holder spaces, is of considerable interest.In this dissertation, we focus on the Hartogs triangle which is a classical source of counterexamples in several complex variables, and generalize it to higher dimensions. We investigate the Lp …
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Regularity theory for nonlocal equations
This thesis is primarily concerned with proving Sobolev regularity results of Calderón-Zygmund-type for nonlinear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients that are merely small in BMO. In particular, such coefficients might be discontinuous.<br …
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Regularity of the D-bar-Neumann Operator, the Bergman Projection and the Canonical Solution Operator of D-bar-Equation
… of these operators is deeply related to the regularity of the $\bar{\partial}$-problem. In this thesis, we focus on the regularity, compactness and boundedness of these operators.</p> <p>In chapter 2, we study the weakly pseudoconvex points on the boundary of a class of Hartogs domains. On …