Studies on nonlinear partial differential equations by potential analysis

点击翻译按钮获取中文摘要

In a bounded smooth domain, we established a suitable boundary growth estimate for positive superharmonic functions satisfying a nonlinear inequality. Moreover, we proved the existence of positive solutions of semilinear elliptic equations that are comparable to the Poisson kernel. Also, we gave a sufficient condition for Dirichlet boundary data to guarantee the existence of positive solutions of singular semilinear elliptic equations. In regard to potential theory, we studied a doubling property of harmonic measure, an estimate for the product of the Green function and the Martin kernel, and the boundary behavior of Martin kernels.