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Variational methods for the numerical solution of nonlinear elliptic problems. (English) Zbl 1333.65065

CBMS-NSF Regional Conference Series in Applied Mathematics 86. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611973-77-8/pbk; 978-1-61197-378-5/ebook). xix, 462 p. (2015).
The book describes the application of variational methods to the solution of nonlinear elliptic problems and has the following contents:
1. On some variational problems in Hilbert spaces;
2. Iterative methods in Hilbert spaces;
3. Operator-splitting and alternating direction methods;
4. Augmented Lagrangians and alternating direction methods;
5. Least squares solution of linear and nonlinear problems in Hilbert spaces;
6. Obstacle problems and Bingham flow: application to control;
7. Nonlinear eigenvalue problems;
8. Eikonal equations;
9. Fully nonlinear elliptic equations.

MSC:

65K10 Numerical optimization and variational techniques
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
49J20 Existence theories for optimal control problems involving partial differential equations
37A15 General groups of measure-preserving transformations and dynamical systems
35J35 Variational methods for higher-order elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J60 Nonlinear elliptic equations
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35F21 Hamilton-Jacobi equations
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