Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE BOUNDARY HARNACK PRINCIPLE IN HÖLDER DOMAINS WITH A STRONG REGULARITY

  • Kim, Hyejin (Department of Mathematics and Statistics University of Michigan-Dearborn)
  • Received : 2015.11.07
  • Published : 2016.11.30
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Abstract

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.

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References

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