Nonlinear Elliptic Partial Differential Equations
Springer International Publishing (Verlag)
978-3-319-78389-5 (ISBN)
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.
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.
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.
| Erscheinungsdatum | 16.06.2018 |
|---|---|
| Reihe/Serie | Universitext |
| Zusatzinfo | X, 253 p. 71 illus., 23 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 409 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | calculus of variations and critical points • calculus of variations and quasilinear problems • direct method calculus of variations • elliptic regularity • Euler-Lagrange Equation • Fixed point theorems • fixed point theorems applications • Galerkin method • Maximum principle • Monotone Operators • mountain pass lemma • nonlinear elliptic partial differential equations • Partial differential equations • polyconvexity • quasiconvexity • rank-1 convexity • superposition operators • super-solutions and sub-solutions • variational inequalities • Young measures |
| ISBN-10 | 3-319-78389-0 / 3319783890 |
| ISBN-13 | 978-3-319-78389-5 / 9783319783895 |
| Zustand | Neuware |
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