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- W2951231317 abstract "The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with $t$-independent complex bounded measurable coefficients ($t$ being the transversal direction to the boundary). To be precise, we show that the Dirichlet boundary value problem is solvable in $L^{p'}$, subject to the square function and non-tangential maximal function estimates, if and only if the corresponding Regularity problem is solvable in $L^p$. Moreover, the solutions admit layer potential representations. In particular, we prove that for any elliptic operator with $t$-independent real (possibly non-symmetric) coefficients there exists a $p>1$ such that the Regularity problem is well-posed in $L^p$." @default.
- W2951231317 created "2019-06-27" @default.
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- W2951231317 date "2013-01-22" @default.
- W2951231317 modified "2023-09-23" @default.
- W2951231317 title "The Regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients" @default.
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