On a Theorem by W. von Wahl

  • M. Uiterdijk

    Delft University of Technology, Netherlands


Let be the - not necessarily densely defined - generator of an analytic semigroup acting in some Banach space . In the paper we prove a general theorem about the existence and uniqueness of solutions of

Our main assumption with respect to the non-linearity is that is locally Lipschitz continuous with respect to certain intermediate spaces between and . Our theorem extends results obtained by W. von Wahl [9] and A. Lunardi [2]. In the second part this theorem is applied to the Cahn-Hilliard equation with Dirichlet boundary conditions.

Cite this article

M. Uiterdijk, On a Theorem by W. von Wahl. Z. Anal. Anwend. 16 (1997), no. 4, pp. 961–978

DOI 10.4171/ZAA/799