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Transactions of the American Mathematical Society

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$ W\sp {2,p}$-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients

Authors: Filippo Chiarenza, Michele Frasca and Placido Longo
Journal: Trans. Amer. Math. Soc. 336 (1993), 841-853
MSC: Primary 35R05; Secondary 35J25
MathSciNet review: 1088476
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Abstract: We prove a well-posedness result in the class $ {W^{2,p}} \cap W_0^{1,p}$ for the Dirichlet problem

$\displaystyle \left\{ {\begin{array}{*{20}{c}} {Lu = f} & {{\text{a.e.}}\;{\tex... ...Omega }, \\ {u = 0} & {{\text{on}}\;\partial \Omega }. \\ \end{array} } \right.$

We assume the coefficients of the elliptic nondivergence form equation that we study are in $ {\text{VMO}} \cap {L^\infty }$ .

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