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Sobolev Spaces, Embedding Theorems and Compactness, Second Order Elliptic Equations, Weak Solutions, Regularity Theorems, Maximum Principles, Eigenvalues, The Principle Eigenvalue, Introduction to Distributions Theory, Variational Methods For Nonlinear Equations. Learning Outcomes# at The End of The Course The Students Will Know# A. Know The Basic Properties of Sobolev Spaces. B. Know How to Apply Variational Methods in Order to Prove Existence Of Weak Solutions to Second Order Elliptic Equations.

Faculty: Mathematics
|Undergraduate Studies |Graduate Studies

Pre-required courses

(104030 - Int.to Partial Differential Equations and 104165 - Real Functions)

• Elliptic partial differential equations of second order - Gilbarg, David
• Functional analysis, Sobolev spaces and partial differential equations - Brézis, H.
• Partial differential equations - Evans, Lawrence C.,