EAN: 9783110250305

PSEUDODIFFERENTIAL AND SINGULAR INTEGRAL OPERAT...

This textbook provides a self-contained and elementary introduction to the modern theory of
pseudodifferential operators and their applications to partial differential equations. In the
first chapters  the necessary material on Fourier transformation and distribution theory is
presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional
Euclidean space is developed. In order to present the deep results on regularity questions for
partial differential equations  an introduction to the theory of singular integral operators is
given - which is of interest for its own. Moreover  to get a wide range of applications  one
chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to
demonstrate some fundamental approaches and the power of the theory  several applications to
wellposedness and regularity question for elliptic and parabolic equations are presented
throughout the book. The basic notation of functional analysis needed in the book is introduced
and summarized in the appendix. The text is comprehensible for students of mathematics and
physics with a basic education in analysis.

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