THE DIRICHLET PROBLEMIN LIPSCHITZ DOMAINS FOR HIGHER ORDER ELLIPTIC SYSTEMSWITH ROUGH COEFFICIENTS

摘要

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefcients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefcients and the unit normal of the boundary belong to the space VMO.