Regularitas Operator Potensial Layer Tunggal

We prove the regularity of the operator Ω∈−= ∫ Ω xdsxxu )()(||ln21)(ξξφξπ ∂ using similar technique for proving Cauchy integral operator. If φ are continue on ∂Ω , we prove that u is uniformly Holder continue in Ω with Holder exponent α for every α ∈ (0,1). However, from the proof, if uL then u is in the same space as before.