The present monograph is devoted to the theory of general parabolic
boundary value problems. The vastness of this theory forced us to
take difficult decisions in selecting the results to be presented
and in determining the degree of detail needed to describe their
proofs. In the first chapter we define the basic notions at the
origin of the theory of parabolic boundary value problems and give
various examples of illustrative and descriptive character. The
main part of the monograph (Chapters II to V) is devoted to a the
detailed and systematic exposition of the L -theory of parabolic 2
boundary value problems with smooth coefficients in Hilbert spaces
of smooth functions and distributions of arbitrary finite order and
with some natural appli cations of the theory. Wishing to make the
monograph more informative, we included in Chapter VI a survey of
results in the theory of the Cauchy problem and boundary value
problems in the traditional spaces of smooth functions. We give no
proofs; rather, we attempt to compare different results and
techniques. Special attention is paid to a detailed analysis of
examples illustrating and complementing the results for mulated.
The chapter is written in such a way that the reader interested
only in the results of the classical theory of the Cauchy problem
and boundary value problems may concentrate on it alone, skipping
the previous chapters."
General
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