Is there a relation between finding  the integral  of derivative function at a singular point lies on boundaries of given domain,  and  define a harmonic function ( u =0 )  on that domain?

 Set , u=0 be a harmonic function  on the given domain such as Crescent domain so there is  a cusp on the its boundaries , how to make this integral bounded < infinite

so if this is happen ...should be u not equal zero!

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