Partial Differential Equations Second Edition /

• Κύριος συγγραφέας: DiBenedetto, Emmanuele (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2010.
• Σειρά: Cornerstones
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Difference equations.; Functional equations.; Fourier analysis.; Integral equations.; Partial differential equations.; Calculus of variations.; Analysis.; Partial Differential Equations.; Fourier Analysis.; Difference and Functional Equations.; Integral Equations.; Calculus of Variations and Optimal Control; Optimization.

 This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists. The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations. Reviews of the first edition: The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs. ---Mathematical Reviews This is a well-written, self-contained, elementary introduction to linear, partial differential equations. ---Zentralblatt MATH. 

 Preliminaries -- Quasi-Linear Equations and the Cauchy#x2013;Kowalewski Theorem -- The Laplace Equation -- Boundary Value Problems by Double-Layer Potentials -- Integral Equations and Eigenvalue Problems -- The Heat Equation -- The Wave Equation -- Quasi-Linear Equations of First-Order -- Non-Linear Equations of First-Order -- Linear Elliptic Equations with Measurable Coefficients -- DeGiorgi Classes.