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001			9780429507069
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006			m o d
007			cr cnu---|nuuu
008			190117s2019 flu ob 001 0 eng d
040			_aOCoLC-P _beng _erda _epn _cOCoLC-P
020			_a9780429016196 _q(electronic bk.)
020			_a0429016190 _q(electronic bk.)
020			_a9780429016202
020			_a0429016204
020			_a9780429507069 _q(electronic bk.)
020			_a0429507062 _q(electronic bk.)
020			_a9780429016189 _q(electronic bk. : Mobipocket)
020			_a0429016182 _q(electronic bk. : Mobipocket)
020			_z9781138580886
020			_z1138580880
024	7		_a10.1201/9780429507069 _2doi
035			_a(OCoLC)1082519168
035			_a(OCoLC-P)1082519168
050		4	_aQA377 _b.S33925 2019eb
072		7	_aMAT _x005000 _2bisacsh
072		7	_aMAT _x034000 _2bisacsh
072		7	_aMAT _x003000 _2bisacsh
072		7	_aMAT _x007000 _2bisacsh
072		7	_aMAT _x021000 _2bisacsh
072		7	_aUB _2bicssc
082	0	4	_a515/.3533 _223
100	1		_aSayas, Francisco-Javier, _eauthor.
245	1	0	_aVariational techniques for elliptic partial differential equations : _btheoretical tools and advanced applications / _cFrancisco J. Sayas, Thomas S. Brown, Matthew E. Hassell.
264		1	_aBoca Raton, Florida : _bCRC Press, _c[2019]
264		4	_c©2019
300			_a1 online resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_aCover; 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)
505	8		_a2.5 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
505	8		_a4.6 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 (*)
505	8		_a6.7 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
505	8		_a8.5 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 (*)
520			_aVariational 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
588			_aOCLC-licensed vendor bibliographic record.
650		0	_aDifferential equations, Elliptic.
650		0	_aDifferential equations, Partial.
650		7	_aMATHEMATICS / Calculus _2bisacsh
650		7	_aMATHEMATICS / Mathematical Analysis _2bisacsh
650		7	_aMATHEMATICS / Applied _2bisacsh
650		7	_aMATHEMATICS / Differential Equations _2bisacsh
650		7	_aMATHEMATICS / Number Systems _2bisacsh
700	1		_aBrown, Thomas S. _c(Mathematician), _eauthor.
700	1		_aHassell, Matthew E., _eauthor.
856	4	0	_3Taylor & Francis _uhttps://www.taylorfrancis.com/books/9780429507069
856	4	2	_3OCLC metadata license agreement _uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999			_c55872 _d55872