Abstract :
Let Ap be a strongly elliptic operator of order 2mŽm N.in L pŽ .Ž1 p
, a bounded domain of Rn. with Dirichlet or Neumann boundary conditions.
Of concern is the Cauchy problem for Schr¨odinger-type evolution equations in
L pŽ .
u Žt. iApuŽt. 0, t R,
½ Ž . uŽ0. u0 .
By showing that iAp is the generator of a C0 group on a certain interpolation
space, we obtain results of wellposedness for Ž ., which are stronger than those
derived from the regularized or integrated groups on L pŽ .. As a by-product, it is
shown that iApis the generator of aŽ Ap. r-regularized groupŽ 0.on
L pŽ . for all
n 1 1 , if1 p ,
r
2m 2 p
n
, if p 1, .
