Final Examination: Monday, June 6, 10:15-12:05, in class. Take-home FINAL EXAM

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Syllabus

Lecture Notes

• Weeks 1-2
  
  
  • Introduction to nonlinear PDEs. Differentiability on Banach spaces, convex functionals.
    
  • Euler-Lagrange equation, examples, existence of minimizers.
  • Some useful remarks.
  
  
• Weeks 3-4
  
  
  • Sufficient Conditions for Existence and Uniqueness. Lagrange Multipliers Theory & Applications
    
  
  
• Weeks 4-5
  
  
  • Mountain Pass Theorem & Applications
    
  
  
• Week 6
  
  
  • Nonvariational techniques: fixed point methods, theorems, and first applications.
    
    
• Weeks 7-8
  
  
  • Applications to Leray-Schauder's theorem. Steady-state Navier-Stokes equations.
    
  • Method of subsolutions and supersolutions.
  
  
• Weeks 9-10
  
  
  • Introduction to nonlinear time-dependent problems.
  
  

Homework assignments