Schrodinger-type evolution equations in Lp(Ω)

Let A(p) be a strongly elliptic operator of order 2m (m is an element of N) in L-p(Omega) (1 less than or equal to p less than or equal to infinity, Omega a bounded domain of R-n) with Dirichlet or Neumann boundary conditions. Of concern is the Cauchy problem for Schrodinger-type evolution equations in L-p(Omega) [GRAPHICS] By showing that iA(p) is the generator of a C-0 group on a certain interpolation space, we obtain results of wellposedness for (*), which arc stronger than those derived from the regularized or integrated groups on L-p(Omega). As a by-product, it is shown that iA(p) is the generator of a (omega + A(p))(-r)-regularized group (omega > 0) on L-p(Omega) for all [GRAPHICS] (C) 2001 Academic Press.