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Weighted elliptic estimates for a mixed boundary system related to the Dirichlet-Neumann operator on a corner domain

  • * Corresponding author: Mei Ming

    * Corresponding author: Mei Ming

The author is supported by NSFC grant 11401598

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  • Based on the $ H^2 $ existence of the solution, we investigate weighted estimates for a mixed boundary elliptic system in a two-dimensional corner domain, when the contact angle $ \omega\in(0,\pi/2) $. This system is closely related to the Dirichlet-Neumann operator in the water-waves problem, and the weight we choose is decided by singularities of the mixed boundary system. Meanwhile, we also prove similar weighted estimates with a different weight for the Dirichlet boundary problem as well as the Neumann boundary problem when $ \omega\in(0,\pi) $.

    Mathematics Subject Classification: Primary: 35Q31, 35J25; Secondary: 35Q35.


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