Partial derivative equation

[UME]

Consider the domain Ω := {x = (x1, x2) ∈ R^2, |x| < 1/2 and x2 > 0}, and we define
also I =] - 1, +1[.
Question 1 :
Does function u1(x) := ln |x| belong to L^2 Ω?
Does it belong to H^1(Ω)?
Compute the u1 standard of L^2(Ω) and u1 of H1(Ω).

Question 2:
Does the function u2(x) := ln | ln |x| | belong to L^2 (Ω) ?
Does it belong to H1 (Ω)? Calculate u2 of L2(Ω) and u2 of H1(Ω).

Question 3:
Does the function u3(x) := ln | ln |x||| belong to L^2 (I) ? Does it belong to H1 (I) ? does it belong to H1/2 (I) ?

 

[HallsofIvy]

When you say u2= |ln|ln|x|| I don't know what you mean by "Calculate u2 of L2(Ω) and u2 of H1(Ω)". Do you mean calculate the integral?

Also what does u3(x)= |ln|ln|x||| mean? Did you mean u3(x)= |ln|ln|ln|x||||?