# Distributions, Sobolev Spaces, Elliptic Equations

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*Dorothee D. Haroske; Hans Triebel*

A publication of the European Mathematical Society

It is the main aim of this book to develop at an accessible, moderate
level an \(L_2\) theory for elliptic differential operators of second
order on bounded smooth domains in Euclidean n-space, including a priori
estimates for boundary-value problems in terms of (fractional) Sobolev spaces
on domains and on their boundaries, together with a related spectral
theory.

The presentation is preceded by an introduction to the classical theory for
the Laplace-Poisson equation, and some chapters provide required ingredients
such as the theory of distributions, Sobolev spaces and the spectral theory in
Hilbert spaces.

The book grew out of two-semester courses the authors have given several
times over a period of ten years at the Friedrich Schiller University of Jena.
It is addressed to graduate students and mathematicians who have a working
knowledge of calculus, measure theory and the basic elements of functional
analysis (as usually covered by undergraduate courses) and who are seeking an
accessible introduction to some aspects of the theory of function spaces and
its applications to elliptic equations.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in differential equations and analysis.