摘要
Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the L^p Dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in Rd is solvable for some 1 < p = p_0 <2(d-1)/(d-2), then it is solvable for all p satisfying ■ The proof is based on a real-variable argument. It only requires that local solutions of L(u) = 0 satisfy a boundary Cacciopoli inequality.
Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the L^p Dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in Rd is solvable for some 1 < p = p_0 <2(d-1)/(d-2), then it is solvable for all p satisfying ■ The proof is based on a real-variable argument. It only requires that local solutions of L(u) = 0 satisfy a boundary Cacciopoli inequality.
基金
Supported in part by NSF(Grant No.DMS-1600520)
