Sobolev regularity theory for the non-local elliptic and parabolic equations on $C^{1,1}$ open sets

Jae-Hwan Choi, Kyeong-Hun Kim, Junhee Ryu

We study the zero exterior problem for the elliptic equation $${\Delta }^{\alpha /2}u-\lambda u=f,x\in D;u{|}_{D^c}=0$$ as well as for the parabolic equation $$ u_t=Δ^{α/2}u+f, \quad t>…