Weighted norm estimates and maximal L_p-regularity
by
Peer Christian Kunstmann
Mathematisches Institut I, Universität Karlsruhe
Coauthors: S. Blunck (Cergy-Pontoise)

Let A be a closed linear operator in a space L_q(\Omega). We give a sufficient condition for maximal L_p-regularity of the evolution equation u'(t) - Au(t) = f(t), t >= 0, u(0)=0. Our condition is in terms of weighted norm estimates for the semigroup (e^tA) and generalizes the assumption that the operators e^tA are integral operators whose kernels satisfy Poisson bounds. As an application we present new results for the maximal regularity of Schrödinger operators, higher order elliptic operators with bounded measurable coefficients, and uniformly elliptic second order operators with singular lower order terms.

Date received: March 13, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-76.