• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.189-195
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• 2015

The goal of this note is to provide a detailed proof for local boundedness estimate near the boundary for weak solutions for second order elliptic equations with bounded measurable coefficients subject to Neumann boundary condition.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1509-1533
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• 2020

We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1741-1751
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• 2016

We prove the boundary Harnack principle and the Carleson type estimate for ratios of solutions u/v of non-divergence second order elliptic equations $Lu=a_{ij}D_{ij}+b_iD_iu=0$ in a bounded domain ${\Omega}{\subset}R_n$. We assume that $b_i{\in}L^n({\Omega})$ and ${\Omega}$ is a $H{\ddot{o}}lder$ domain of order ${\alpha}{\in}$ (0, 1) satisfying a strong regularity condition.