Elliptic Differential Operators and Spectral Analysis

• Main Authors: Edmunds, D. E. (Author, http://id.loc.gov/vocabulary/relators/aut), Evans, W.D (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Springer Monographs in Mathematics,
• Subjects: Partial differential equations.; Differential equations.; Functional analysis.; Operator theory.; Partial Differential Equations.; Ordinary Differential Equations.; Functional Analysis.; Operator Theory.

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally assoc...

Table of Contents:

• 1. Preliminaries
• 2. The Laplace Operator
• 3. Second-order elliptic equations
• 4. The classical Dirichlet problem for second-order elliptic operators
• 5. Elliptic operators of arbitrary order
• 6. Operators and quadratic forms in Hilbert space
• 7. Realisations of second-order linear elliptic operators
• 8. The Lp approach to the Laplace operator
• 9. The p-Laplacian
• 10. The Rellich inequality
• 11. More properties on Sobolev embeddings
• 12. The Dirac Operator.