MATS340 Partial Differential Equations 2 (5 cr)

Sobolev spaces and inequalities (review), elliptic partial differential equations in divergence form and their weak solutions, existence of solutions, maximum and comparison principles, uniqueness of solutions, regularity of solutions, parabolic partial differential equations and their weak solutions

• is able to use basic tools of Sobolev spaces in dealing with partial differential equations 
  
• knows the weak definition of a solution to a partial differential equation and can verify in simple cases that a given function is a weak solution
  
• recognizes elliptic and parabolic partial differential equations and knows applicable existence, uniqueness and regularity results and techiques
  
• can apply the results for partial differential equations
  

The course falls within the field of partial differential equations:other courses Partial Differential Equations 1A and 1B, as well as Viscosity Theory). Partial Differential Equations 2 and Viscosity Theory can be taken in any order.

Partial differential equations 1A and 1B. Sobolev spaces is recommended but the theory of Sobolev spaces is briefly reviewed at the beginning, and it can be self-studied as well if one has taken Measure and integration 1.

Lecture notes.