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

eigenvalues.

Textbook:

Craig Evans: Partial Differential Equations

Reference:

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%