Everitt W.N., Markus L. Elliptic Partial Differential Operators and Symplectic Algebra

American Mathematical Society, 2003. — 117 p. — (Memoirs of the American Mathematical Society 770). — ISBN13: 978-0821832356.This investigation introduces a new description and classification for the set of all self-adjoint operators (not just those defined by differential boundary conditions) which are generated by a linear elliptic partial differential expression.
The scope of the theory is illustrated by several familiar, and other quite unusual, self-adjoint operators described in special examples. An Appendix is attached to present the basic definitions and concepts of differential topology and functional analysis on differentiable manifolds.
An Appendix is attached to present the basic definitions and concepts of differential topology and functional analysis on differentiable manifolds. In this Appendix care is taken to list and explain all special mathematical terms and symbols - in particular, the notations for Sobolev Hilbert spaces and the appropriate trace theorems.Elliptic partial differential operators and symplectic algebra
Introduction: Organization of results
Review of Hilbert and symplectic space theory
GKN-theory for elliptic differential operators
Examples of the general theory
Global boundary conditions: Modified Laplace operators88
Appendix A. List of symbols and notations