Weighted Sobolev space theory for non-local elliptic and parabolic equations with non-zero exterior condition on $C^{1,1}$ open sets

Kyeong-Hun Kim, Junhee Ryu

We introduce a weighted Sobolev space theory for the non-local elliptic equation $$\hat{I}{”}^{\hat{I}\pm /2}u=f,x\in \mathcal{O};r_{{\overline{\mathcal{O}}}^c}u=g$$ as well as for…