Nonlinear Elliptic Partial Differential Equations An Introduction /

• Main Author: Le Dret, Hervé (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Universitext,
• Subjects: Partial differential equations.; Calculus of variations.; Functional analysis.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.; Functional Analysis.
• Physical Description: X, 253 p. 71 illus., 23 illus. in color. online resource.
• ISBN: 9783319783901
• ISSN: 0172-5939
• DOI: 10.1007/978-3-319-78390-1

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.