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