عنوان

Variational techniques for elliptic partial differential equations :

شابک

0429016182

شابک

0429016190

شابک

0429016204

شابک

0429507062

شابک

9780429016189

شابک

9780429016196

شابک

9780429016202

شابک

9780429507069

شابک اشتباه

1138580880

شابک اشتباه

9781138580886

عنوان اصلي

Variational techniques for elliptic partial differential equations :

نام عام مواد

[Book]

ساير اطلاعات عنواني

theoretical tools and advanced applications /

نام نخستين پديدآور

Francisco J. Sayas, Thomas S. Brown, Matthew E. Hassell.

محل نشرو پخش و غیره

Boca Raton, Florida :

نام ناشر، پخش کننده و غيره

CRC Press,

تاریخ نشرو بخش و غیره

[2019]

تاریخ نشرو بخش و غیره

©2019

نام خاص و کميت اثر

1 online resource

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Preface; Authors; Part I: Fundamentals; 1. Distributions; 1.1 The test space; 1.2 Distributions; 1.3 Distributional differentiation; 1.4 Convergence of distributions; 1.5 A fundamental solution (*); 1.6 Lattice partitions of unity; 1.7 When the gradient vanishes (*); 1.8 Proof of the variational lemma (*); Final comments and literature; Exercises; 2. The homogeneous Dirichlet problem; 2.1 The Sobolev space H1(O); 2.2 Cuto and molli cation; 2.3 A guided tour of mollification (*); 2.4 The space H10(O)

متن يادداشت

2.5 The Dirichlet problem2.6 Existence of solutions; Final comments and literature; Exercises; 3. Lipschitz transformations and Lipschitz domains; 3.1 Lipschitz transformations of domains; 3.2 How Lipschitz maps preserve H1 behavior (*); 3.3 Lipschitz domains; 3.4 Localization and pullback; 3.5 Normal elds and integration on the boundary; Final comments and literature; Exercises; 4. The nonhomogeneous Dirichlet problem; 4.1 The extension theorem; 4.2 The trace operator; 4.3 The range and kernel of the trace operator; 4.4 The nonhomogeneous Dirichlet problem; 4.5 General right-hand sides

متن يادداشت

4.6 The Navier-Lamé equations (*)Final comments and literature; Exercises; 5. Nonsymmetric and complex problems; 5.1 The Lax-Milgram lemma; 5.2 Convection-di usion equations; 5.3 Complex and complexified spaces; 5.4 The Laplace resolvent equations; 5.5 The Ritz-Galerkin projection (*); Final comments and literature; Exercises; 6. Neumann boundary conditions; 6.1 Duality on the boundary; 6.2 Normal components of vector fields; 6.3 Neumann boundary conditions; 6.4 Impedance boundary conditions; 6.5 Transmission problems (*); 6.6 Nonlocal boundary conditions (*)

متن يادداشت

6.7 Mixed boundary conditions (*)Final comments and literature; Exercises; 7. Poincar e inequalities and Neumann problems; 7.1 Compactness; 7.2 The Rellich-Kondrachov theorem; 7.3 The Deny-Lions theorem; 7.4 The Neumann problem for the Laplacian; 7.5 Compact embedding in the unit cube; 7.6 Korn's inequalities (*); 7.7 Traction problems in elasticity (*); Final comments and literature; Exercises; 8. Compact perturbations of coercive problems; 8.1 Self-adjoint Fredholm theorems; 8.2 The Helmholtz equation; 8.3 Compactness on the boundary; 8.4 Neumann and impedance problems revisited

متن يادداشت

8.5 Kirchho plate problems (*)8.6 Fredholm theory: the general case; 8.7 Convection-diffusion revisited; 8.8 Impedance conditions for Helmholtz (*); 8.9 Galerkin projections and compactness (*); Final comments and literature; Exercises; 9. Eigenvalues of elliptic operators; 9.1 Dirichlet and Neumann eigenvalues; 9.2 Eigenvalues of compact self-adjoint operators; 9.3 The Hilbert-Schmidt theorem; 9.4 Proof of the Hilbert-Schmidt theorem (*); 9.5 Spectral characterization of Sobolev spaces; 9.6 Classical Fourier series; 9.7 Steklov eigenvalues (*); 9.8 A glimpse of interpolation (*)

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

متن يادداشت

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

منبع سفارش / آدرس اشتراک

Ingram Content Group

شماره انبار

9780429016196

شماره استاندارد بين المللي کتاب و موسيقي

9781138580886

موضوع مستند نشده

Differential equations, Elliptic.

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Differential equations, Elliptic.

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

MATHEMATICS-- Applied.

موضوع مستند نشده

MATHEMATICS-- Calculus.

موضوع مستند نشده

MATHEMATICS-- Differential Equations.

موضوع مستند نشده

MATHEMATICS-- Mathematical Analysis.

موضوع مستند نشده

MATHEMATICS-- Number Systems.

موضوع مستند نشده

MAT-- 003000

موضوع مستند نشده

MAT-- 005000

موضوع مستند نشده

MAT-- 007000

موضوع مستند نشده

MAT-- 021000

موضوع مستند نشده

MAT-- 034000

موضوع مستند نشده

UB

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Sayas, Francisco-Javier

مستند نام اشخاص تاييد نشده

Brown, Thomas S., (Mathematician)

مستند نام اشخاص تاييد نشده

Hassell, Matthew E.

تاريخ عمليات

20200822112110.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y