MATS424 Viscosity Theory (5–10 cr)

Definition of a viscosity solution, uniformly elliptic non divergence form equation, comparison principle and uniqueness, existence of a solution, regularity results.

• knows the definition of the viscosity solution
  
• recognizes to which partial differential equations the theory applies 
  
• knows central existence, uniqueness, and regularity results and techniques and can apply these in the example problems
  

The course falls within the field of partial differential equations (other courses Partial Differential Equations 1A and 1B, as well as Partial Differential Equations 2). The course can also be taken before Partial Differential Equations 2 -course.

Partial differential equations 1A and 1B

Lecture notes.

Additional literature: 

Evans: Partial differential equations, 

Koike: Beginners guide to the theory of viscosity solutions, 

Caffarelli, Cabre: Fully nonlinear elliptic equations