The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients

摘要

We study the Dirichlet problem in Lipschitz domains and with boundary data inBesov spaces, for divergence form strongly elliptic systems of arbitrary order,with bounded, complex-valued coefficients. Our main result gives a sharpcondition on the local mean oscillations of the coefficients of thedifferential operator and the unit normal to the boundary (which isautomatically satisfied if these functions belong to space VMO) guaranteeingthat the solution operator associated with this problem is an isomorphism.