Partial Differential Equations

Third Auflage 2023
ISBN: 978-3-031-46617-5
Verlag: Birkhäuser

Buch, Englisch, 748 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1320 g

Reihe: Cornerstones

This book offers a self-contained introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing perspective on nonlinear equations. The treatment is mathematically rigorous with a generally theoretical layout, with indications to some of the physical origins of PDEs. The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding. Requiring only advanced differential calculus and some basic L theory, the book will appeal to advanced undergraduates and graduate students, and to applied mathematicians and mathematical physicists.

Zielgruppe

Graduate

Autoren/Hrsg.

Dibenedetto, Emmanuele

Gianazza, Ugo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

Preliminaries.- Quasi-Linear Equations and the Cauchy-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.- Linear Elliptic Equations with Measurable Coefficients.- Elliptic De Giorgi Classes.- Navier-Stokes Equations.- Quasi-Linear Hyperbolic First Order Systems.- Non-Linear Equations of the First Order.

Über Autor(innen)

Emanuele DiBenedetto (1947-2021) was Emeritus Centennial Professor of Mathematics at Vanderbilt University. His teaching and research at Vanderbilt focused on the study of partial differential equations, particularly the elliptic and parabolic ones. He was a prolific writer, authoring more than 120 papers and six books. He served as editor-in-chief of the Journal on Mathematical Analysis of the Society for Industrial and Applied Mathematics. In addition, he was on more than twenty editorial boards and gave numerous invited talks.
Ugo Gianazza is Professor of Mathematical Analysis at the Department of Mathematics F. Casorati of the University of Pavia. His research interests include Regularity for Elliptic and Parabolic Equations. In addition to editing numerous volumes, he also co-authored the 2012 monograph Harnack's Inequality for Degenerate and Singular Parabolic Equation.