Dirichlet problem for higher order elliptic systems with BMO assumptions on the coefficients and the boundary

Dirichlet problem for higher order elliptic systems with BMO assumptions on the coefficients and the boundary

Mon, 23/11/2009
13:00 		Tatyana Shaposhnikova (Linköping University, Sweden) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Dirichlet problem for higher order elliptic systems with BMO assumptions on the coefficients and the boundary
Given a bounded Lipschitz domain, we consider the Dirichlet problem with boundary data in Besov spaces for divergence form strongly elliptic systems of arbitrary order with bounded complex-valued coefficients. The main result gives a sharp condition on the local mean oscillation of the coefficients of the differential operator and the unit normal to the boundary (automatically satisfied if these functions belong to the space VMO) which guarantee that the solution operator associated with this problem is an isomorphism.