1.

Record Nr.

UNINA9910300118503321

Autore

Edmunds D. E (David Eric)

Titolo

Elliptic Differential Operators and Spectral Analysis [[electronic resource] /] / by D. E. Edmunds, W.D. Evans

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018

ISBN

3-030-02125-4

Edizione

[1st ed. 2018.]

Descrizione fisica

1 online resource (x, 310 pages)

Collana

Springer Monographs in Mathematics, , 1439-7382

Disciplina

515.353

Soggetti

Partial differential equations

Differential equations

Functional analysis

Operator theory

Partial Differential Equations

Ordinary Differential Equations

Functional Analysis

Operator Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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 associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space



and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.