Rev. R. Acad. Cien. Serie A. Mat.
VOL. 95 (1), 2001, pp. 85119
Matem´atica Aplicada/Applied Mathematics
Linear parabolic problems involving measures
Abstract We develop a general solvability theory for linear evolution equations of the form £¤¦¥¨§©¤
on , where § is the infinitesimal generator of a strongly continuous analytic semigroup, and is
a bounded Banach-space-valued Radon measure. It is based on the theory of interpolation-extrapolation
spaces and the Riesz representation theorem for such measures.
The abstract results are illustrated by applications to second order parabolic initial value problems.
In particular, the case where Radon measures occur on the Dirichlet boundary can be handled, which is
important in control theory and has not been treated so far.
We also give sharp estimates under various regularity assumptions. They form the basis for the study
of semilinear parabolic evolution equations with measures to be studied in a forthcoming paper jointly
with P. Quittner.
Problemas lineales parab´olicos involucrando medidas
Resumen Desarrollamos una teor´ia general para la resoluci´on de ecuaciones lineales de evoluci´on
de la forma £¤¦¥¨§©¤ sobre , donde § es el generador infinitesimal de un semigrupo anal´itico