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The optimal weighted $W^{2, p}$ estimates of elliptic equation with non-compatible conditions

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  • In this paper we study uniformly elliptic equations with non-compatible conditions, where $\Omega$ is a bounded Lipchitz domain, and the right-hand side term and the boundary value of the elliptic equations belong to $L^p (p \geq 2)$ space. Then the optimal weighted $W^{2, p}$ estimates will be given by Whitney decomposition and $L^p$ estimates of non-tangential maximal function associated to solutions of the elliptic equations.
    Mathematics Subject Classification: Primary: 35J17, 35J60; Secondary: 47B25.


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