讲座内容简介:
In 1924, Wiener established the well known criterion on the harmonic extension of continuous data on rough domains. In this talk, I will review known results on the Wiener criterion for elliptic and parabolic equations. Estimates of modulus of continuity for solutions at the boundary will be given in terms of a Wiener-type integral, defined by a notion of capacity. In particular, some recent advances on such estimates for solutions to singular or degenerate parabolic equations will be reported.

讲座人简介：
廖乃安博士毕业于美国Vanderbilt大学，现任教于重庆大学数学系，研究方向为偏微分方程。先后在Discrete Contin. Dyn. Syst.， Nonlinear Anal.，Manuscripta Math.,  Riv. Math. Univ. Parma (N.S.)，NoDEA Nonlinear Differential Equations Appl.， Ann. Acad. Sci. Fenn. Math. 等知名数学杂志发表论文多篇。现主持国家自然科学基金青年基金一项。