Short Introduction to Partial Differential Equations

The author is a professor of Mathematics at University of Ottawa, Canada (since 2002). He holds a PhD in Mathematics from University Henri Poincare, Nancy, France, 1997. Before joining University of Ottawa in 2002, he had held postdoctoral positions at INRIA France and PIMS, UBC, Vancouver, Canada. The author's main research area are Shape Optimization and Partial Differential Equations, as they are integral part of his research. The author has taught PDEs at University of Ottawa for many years, and this book represents this teaching experience.

“The book will serve as a guide for researchers by helping them with essential results for progressing their research. There are many examples, which will certainly help a reader in grasping the key ideas. … The book gives good insight into the fundamental key concepts, results and techniques and is therefore useful equally for beginners, veterans and researchers.” (Urvashi Arora, Mathematical Reviews, February, 2025)

• 1 Notations and review.- 2 Partial differential equations.- 3 First order PDEs. Classical and weak solutions.- 4 Second-order linear elliptic PDEs. maximum principle and classical solutions - 5 Distributions.- 6 Sobolev spaces.- 7 Second order linear elliptic PDEs. Weak solutions.- 8 Second order parabolic and hyperbolic PDEs.- 9 Annex.