Second-order parabolic partial differential equation

Author: Chen Yazi
Publisher:
Publish Date: 2003-01-01
Features: This book systematically presents the fundamental theory, methods, and applications of second-order parabolic partial differential equations. The book is divided into nine chapters. The content includes Campanato spaces, Sobolev spaces (anisotropic with respect to x and t), the existence and uniqueness of weak solutions, Schauder theory, Lp theory, DeGiorgi-Nash-Moser estimates, Krylov-Safonov estimates, divergence-type quasilinear equations, and fully nonlinear equations. The book provides a relatively complete introduction to the application of Campanato spaces in second-order parabolic partial differential equations. It first introduces the Campanato space related to parabolic distance and uses it as a tool to establish the embedding theorem for the anisotropic Sobolev space Wp2,1 with respect to x and t. It then builds the Schauder theory and Lp theory for parabolic equations. Finally, it combines these theories with DeGiorgi-Nash-Moser estimates to prove the rich regularity of solutions to divergence-type quasilinear parabolic equations. For non-divergence-type general equations, it introduces Krylov-Safonov estimates and uses them to discuss fully nonlinear equations. This book can serve as a textbook or teaching reference for senior undergraduate and graduate students in mathematics, applied mathematics, mechanics, and physics departments of comprehensive universities and advanced normal universities. It is also a valuable learning reference for mathematicians and scientific and technological workers engaged in the field of partial differential equations.