報告一：Examples of twice differentiable functions with continuous Laplacian and unbounded Hessian

　　報告時間：5月14日-16日15:30-17:30   地點: 1-423

　　摘要：We construct examples of twice differentiable functions in R^n with continuous Laplacian and unbounded Hessian. The same construction is also applicable to higher order differentiability.

　　報告二：Counterexamples for Calderón-Zygmand estimates via holomorphic function in C^n

　　報告時間：5月22日-24日15:30-17:30   地點: 1-423

　　摘要：The Calderón-Zygmand theory says that for Δu=f, if f belongs to L^p then u belongs to W^{2, p}. It is well known that the case of p=1 fails. We show that for any holomorphic function, we construct an example showing the theory fails when . This provided abundant examples than the classical one.

　　報告三：The local regularity of Beurling operator in complex plane

　　報告時間：6月4日-6日15:30-17:30   地點:1-423

　　摘要：Let B(z) be the Beurling operator that is defined on L^p. We show that  B(z) preserves smoothness of locally.

　　報告人簡介：潘一飛，美國印第安納普渡大學教授，博士生導師；從事多復變、復分析和偏微分方程等領域的研究工作，在Duke. Math、Tran. Amer. Math. Soc.、Ann. Fac. Sci. Toulouse Math.等期刊發表學術論文60余篇。