Partial Differential Equations

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.

“This is the third edition of a book In this third edition a good deal of new and more advanced material has been added ... . From edition to edition, this book has evolved into a rather specialized text. It is likely to be of more interest now to specialists than students new to the study of PDEs.” (Bill Satzer, MAA Reviews, February 29, 2024)

• 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.