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By convention whenever n 2 1 and x,y e R", we write | x1 = Vx} + ... + x}; and (x, y) =) Σ Xiyi. i=1 = c) Assume that u
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By convention whenever n 2 1 and x,y e R", we write | x1 = Vx} + ... + x}; and (x, y) =) Σ Xiyi. i=1 = c) Assume that u
By convention whenever n 2 1 and x,y e R", we write | x1 = Vx} + ... + x}; and (x, y) =) Σ Xiyi. i=1 = c) Assume that u € C²(82%) n c°(92*) is harmonic such that lim 1-0 log in (x) Uc = limx- u(x) exists with 0. Show that изо 1 21 Ś u(cos(O), sin(O))do. Hint: You may use the removable singularity theorem. d) Show that there is no harmonic function u € C-(92%) n (22") with lim. u(x) = 0 and u(w) = 1 for all w with \w] = 1.