Partial Differential Equations

Provides a self-contained introduction to the classical theory of partial differential equations (PDEs) Expands on the Second Edition with five new chapters, as well as new exercises and examples Examines how the classical approach to PDEs connects to cutting-edge research and the modeling of physical phenomena

Autorentext

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.

Klappentext

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 Lp theory, the book will appeal to advanced undergraduates and graduate students, and to applied mathematicians and mathematical physicists.

Inhalt
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.