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Chiun-Chang Lee

2011-12-02
15:10:00 - 16:40:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The Robin function R(x) due to the regular part of the harmonic Green function plays an important role in many applications. For instance, blow-up points in a single bubble solution of the Liouville equation and a single vortex solution of the Ginzburg-Landau equation are all determined by the critical points of R(x). In this talk, we will follow the work of Juan Davila et. al. [cf. Journal of Functional Analysis 255, pp. 1057-1101] to show that the harmonic Robin function R(x) with the Robin boundary condition possesses at least 3 critical points, which is different from the harmonic Robin function with the Dirichlet boundary condition.