integral equation

[lldk]

I don't know how to start this question. Could somebody help me or give me some hints?

 

[Deleted member 4993]

I don't know how to start this question. Could somebody help me or give me some hints?

You should know that

(f(x) -1)² (without absolute value sign ) is always > = 0. Continue.....

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[blamocur]

Can you prove that
[math]\int_\Omega (g(x))^2 dx = 0 \Rightarrow g \equiv 0 \;\text{on}\; \Omega[/math]