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

Maz'ya, Vladimir; Mitrea, Marius; Shaposhnikova, Tatyana

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

Authors

Maz'ya, Vladimir

Mitrea, Marius

Shaposhnikova, Tatyana

Description

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 coefficients. Our main result gives a sharp condition on the local mean oscillations of the coefficients of the differential operator and the unit normal to the boundary (which is automatically satisfied if these functions belong to space VMO) guaranteeing that the solution operator associated with this problem is an isomorphism.
revised version