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Wei-Chung Chen (TIMS)
2015-02-06 10:00:00 - 12:20:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In solving 1st order linear PDEs via L² estimate, the density in the graph norm of smooth members in the domain of the strong extension of 1st order linear differential operators is crucial. The aforementioned density in the boundary-free case was due to K. O. Freidrichs in 1944 by convolution with smooth mollifiers. In 1965, the case with boundary was settled by L. Hörmander by convolution with skewed mollifiers and with suitable measures. The case with boundary is necessary in the theory of several complex variables and in complex algebraic geometry. In this talk, we will report on Hörmander's approach. Reference: L. Hörmander's, L² estimates and existence theorems for the operator, Acta Math., 113 (1965) (Part I, Sec. 1.2)