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(Solved): 3 Prove the following positivity statement (Exercise 6.4.1): Let U be a connected domain in R^(n), a ...
3
Prove the following positivity statement (Exercise 6.4.1): Let U be a connected domain in R^(n), and suppose
uinC^(2)(U)\cup C(()/(bar) (U)) satisfies
-\Delta u=0 in U
u=g on delU
Assume that g>=0, and further g(y)>0 for some yindelU. Prove that u(x)>0 for all xinU.