Elliptic Differential Operators and Spectral Analysis. 1st ed. 2018

種類:

電子ブック

責任表示:

by D. E. Edmunds, W.D. Evans

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Edmunds, D. E.
• Evans, W.D.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783030021252 [3030021254]    

注記:

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.
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 uni

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