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Nonlinear Elliptic Partial Differential Equations: An Introduction de Hervé Le Dret

Nonlinear Elliptic Partial Differential Equations: An Introduction: Universitext

Autor Hervé Le Dret
en Limba Engleză Paperback – 5 iun 2018
This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.
After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations.
Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.


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Specificații

ISBN-13: 9783319783895
ISBN-10: 3319783890
Pagini: 253
Ilustrații: X, 253 p. 71 illus., 23 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 4.04 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Cuprins

1 A brief review of real and functional analysis.- 2 Fixed point theorems and applications.- 3 Superposition operators.- 4 The Galerkin method.- 5 The maximum principle, elliptic regularity, and applications.- 6 Calculus of variations and quasilinear problems.- 7 Calculus of variations and critical points.- 8 Monotone operators and variational inequalities.- References.- Index.

Notă biografică

Hervé Le Dret is Professor of Mathematics at the Laboratoire Jacques-Louis Lions, Sorbonne Université, Paris, France. He recently completed two consecutive five-year terms as Dean of the Faculty of Mathematics and is now back to regular teaching and research duties. His research focuses on partial differential equations in mechanics, calculus of variations and numerical analysis.

Textul de pe ultima copertă

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.

After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations.
Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

Caracteristici

Introduces several mathematical techniques relevant to solving boundary value problems involving nonlinear elliptic PDEs Provides the essentials of test-function and distribution spaces Includes 44 exercises and problems