UID:
almahu_9949462112002882
Format:
1 online resource (834 p.)
ISBN:
9783110269291
,
9783110238570
Series Statement:
De Gruyter Textbook
Content:
This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc., who were interested in studying the problems of mathematical physics in general and their approximate solutions on computer in particular. Almost all topics which will be essential for the study of Sobolev spaces and their applications in the elliptic boundary value problems and their finite element approximations are presented. Also many additional topics of interests for specific applied disciplines and engineering, for example, elementary solutions, derivatives of discontinuous functions of several variables, delta-convergent sequences of functions, Fourier series of distributions, convolution system of equations etc. have been included along with many interesting examples.
Note:
Frontmatter --
,
Preface --
,
Contents --
,
How to use this book in courses --
,
Acknowledgment --
,
Notation --
,
Chapter 1. Schwartz distributions --
,
Chapter 2. Differentiation of distributions and application of distributional derivatives --
,
Chapter 3. Derivatives of piecewise smooth functions, Green's formula, elementary solutions, applications to Sobolev spaces --
,
Chapter 4. Additional properties of Dʹ(Ω) --
,
Chapter 5. Local properties, restrictions, unification principle, space ℰʹ(ℝn) of distributions with compact support --
,
Chapter 6. Convolution of distributions --
,
Chapter 7. Fourier transforms of functions of L1(ℝn) and S(ℝn) --
,
Chapter 8. Fourier transforms of distributions and Sobolev spaces of arbitrary order HS(ℝn) --
,
8.1 Motivation for a possible definition of the Fourier transform of a distribution --
,
8.2 Space Sʹ (Rn) of tempered distributions --
,
8.3 Fourier transform of tempered distributions --
,
8.4 Fourier transform of distributions with compact support --
,
8.5 Fourier transform of convolution of distributions --
,
8.6 Derivatives of Fourier transforms and Fourier transforms of derivatives of tempered distributions --
,
8.7 Fourier transform methods for differential equations and elementary solutions in Sʹ(ℝn) --
,
8.8 Laplace transform of distributions on ℝ --
,
8.9 Applications --
,
8.10 Sobolev spaces on Ω ≠ Rn revisited --
,
8.11 Compactness results in Sobolev spaces --
,
8.12 Sobolev's imbedding results --
,
8.13 Sobolev spaces Hs.(Γ), Ws;p(Γ) on a manifold boundary Γ --
,
8.14 Trace results in Sobolev spaces on Ω⊊ℝn --
,
Chapter 9. Vector-valued distributions --
,
Appendix A. Functional analysis (basic results) --
,
Appendix B. Lp-spaces --
,
Appendix C. Open cover and partition of unity --
,
Appendix D. Boundary geometry --
,
Bibliography --
,
Index
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012, De Gruyter, 9783110288995
In:
E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012, De Gruyter, 9783110293722
In:
E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012, De Gruyter, 9783110288926
Additional Edition:
ISBN 9783110269277
Language:
English
DOI:
10.1515/9783110269291
URL:
https://doi.org/10.1515/9783110269291
URL:
https://www.degruyter.com/isbn/9783110269291
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