$W^ {2,p}$-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients
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- by Filippo Chiarenza, Michele Frasca and Placido Longo PDF
- Trans. Amer. Math. Soc. 336 (1993), 841-853 Request permission
Abstract:
We prove a well-posedness result in the class ${W^{2,p}} \cap W_0^{1,p}$ for the Dirichlet problem \[ \left \{ {\begin {array}{*{20}{c}} {Lu = f} & {{\text {a.e.}}\;{\text {in}}\;\Omega }, \\ {u = 0} & {{\text {on}}\;\partial \Omega }. \\ \end {array} } \right .\] We assume the coefficients of the elliptic nondivergence form equation that we study are in ${\text {VMO}} \cap {L^\infty }$ .References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 336 (1993), 841-853
- MSC: Primary 35R05; Secondary 35J25
- DOI: https://doi.org/10.1090/S0002-9947-1993-1088476-1
- MathSciNet review: 1088476