By Convention Whenever N 2 1 And X Y E R We Write N X Vx X And X Y Xiyi I 1 C Assume That U C 1 (12.82 KiB) Viewed 44 times
By Convention Whenever N 2 1 And X Y E R We Write N X Vx X And X Y Xiyi I 1 C Assume That U C 2 (47.34 KiB) Viewed 44 times
By convention whenever n 2 1 and x,y e R", we write n [x] = Vx . + x} and (x, y) = { xiyi = i=1
c) Assume that u € C?(92“) n C°(22") is harmonic such that limix|-100 un = lim x1- 4(x) exists with (x) log |x -0. Show that U.. = 21 S. Sºucos(9), sino)do. Hint: You may use the removable singularity theorem. d) Show that there is no harmonic function u € C?(92%) n C°(7") with lim.:- (x) = 0) and u(w) = 1 for all w with \w] = 1.
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