学术报告（Seick Kim 2025.4.22）

摘要: In this talk, we discuss the Dirichlet problem for a non-divergence form elliptic operator L in a bounded domain. Under certain conditions on the coefficients of L, we establish the existence of a unique Green’s function in a ball and derive two-sided pointwise estimates for it. Using these results, we show that regular points for L coincide with those for the Laplace operator, as characterized by the Wiener test. This equivalence ensures the unique solvability of the Dirichlet problem with continuous boundary data in regular domains. Additionally, we construct the Green’s function for L in regular domains and establish pointwise bounds for it.