In this one-semester course we shall restrict our attention to the theory of second order elliptic equations.
The contents are followings:
(1) Laplace Equation: Fundamental solution, Mean-Value formula,Properties of harmonic functions, Green's
functions, Energy method.
(2)Second Order Elliptic Equations : Weak Solutions, Lax-Mailgram Theorem, Maximum Principle, Eigenvalues
and eigenfunctions
(3)The method of upper and lower solutions, The moving plane method, Krein-Rutman Theorem and Principal

Craig Evans: Partial Differential Equations

Lopez-Gomez J. : Second order linear elliptic equations
Yi-Hong Du: Order Structure and topological methods in nonlinear partial differential equations.

Grading Policy:
Homework : 30%
Midterm Exam. 35%
Final exam. 35%