Analytical Pde Theory

Analytical PDE Theory is a set of original Brown University lecture notes, problems, solutions, theorems and more on the analytical theory of linear and nonlinear partial differential equations (PDE), inspired by the lectures of Professor Walter A. Strauss, Ph.D. in 2001. These notes cover the following topics:* Regularity and weak solutions, including the boundary* 2nd and Higher Order Elliptic Equations, including Elliptic estimates* Distributions and characteristics and other fundamentals* Hyperbolic PDE theory and systems, including the Paley-Wiener Theorem for infinitely continuous functions* Nonlinear PDE and Kinetic Theory * Vlasov Equation and Vlasov-Poisson System, including plasma of electrons and semiconductors* Energy invariants, global weak solutions and more