In this one-semester course we shall restrict our attention to the theory of second order elliptic equations.
<br>The contents are followings:
<br>(1) Laplace Equation: Fundamental solution, Mean-Value formula,Properties of harmonic functions, Green's     
<br>     functions, Energy method.
<br>(2)Second Order Elliptic Equations : Weak Solutions, Lax-Mailgram Theorem, Maximum Principle, Eigenvalues 
<br>     and eigenfunctions
<br>(3)The method of upper and lower solutions, The moving plane method, Krein-Rutman Theorem and Principal 
<br>     eigenvalues.
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<br>Textbook:
<br>Craig Evans: Partial Differential Equations
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<br>Reference:
<br>Lopez-Gomez J. : Second order linear elliptic equations
<br>Yi-Hong Du: Order Structure and topological methods in nonlinear partial differential equations.
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<br>Grading Policy:
<br>      Homework : 30%
<br>      Midterm Exam. 35%
<br>      Final exam. 35%
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