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NONAUTONOMOUS PARABOLIC EQUATIONS INVOLVING MEASURES
 

Summary: NONAUTONOMOUS PARABOLIC EQUATIONS
INVOLVING MEASURES
H. AMANN
Dedicated to V.A. Solonnikov for his 70th
birthday
Summary: In the first part of this paper we study abstract parabolic evolution
equations involving Banach space valued measures. These results are applied
in the second part to second order parabolic systems under minimal regularity
hypotheses on the coefficients.
Introduction
In [5] we developed a solvability and regularity theory for abstract par-
abolic evolution equations of the form
u + Au = µ in J. (0.1)
Here -A generates an analytic semigroup on some Banach space E, and
µ is a bounded Radon measure on a bounded interval J, taking values in
a suitable intermediate space between E and the domain of A. In that
paper it is also shown that the general theory applies to linear parabolic
boundary value problems of the form
tu + Au = µ in × J,
Bu = µ on × J,

  

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics