MATH 516 Midterm: MATH 516 2008 Winter Test 1
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U := ( 1, 1) ( 1, 1) := {(x, y) r2 such that 1 < x < 1, 1 < y < 1}, and u = 1 2 with. 1 := ({ 1} {1}) ( 1, 1) = {(x, y) r2 such that |x| = 1, 1 < y < 1}. 2 := ( 1, 1) ({ 1} {1}) = {(x, y) r2 such that |y| = 1, 1 < x < 1}. and we want to solve on u the following equation, with f l2(u ): U = f in u u = 0 on 1. E := {u c ( u ) such that supp(u) 1 = } H := {u h 1(u ) such that u| 1 = 0}: show that the closure of e in h 1(u ) is h, prove the following poincar e inequality.
