On boundary behavior of harmonic functions in Hölder domains
Let \(L\) denote a uniformly elliptic operator with bounded coefficients on a Hölder domain \(D\). Using probabilistic techniques, \textit{R. Bañuelos, R. F. Bass} and \textit{K. Burdzy} [Duke Math. J. 64, No. 1, 195-200 (1991; Zbl 0755.35027)] proved a boundary Harnack principle for \(L\)-harmonic functions on \(D\). In the paper under review, assuming that \(L\) has smooth coefficients, the author proves the same result by purely analytic methods; the estimates obtained do not depend on the smoothness of the coefficients. Results about \(L\)-harmonic measure on \(\partial D\) are also proved, notably a doubling property.
scientific article; zbMATH DE number 1269731