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Learning outcomes

After taking the course a student:
-knows different definitions of the Sobolev spaces and recognizes Sobolev functions using them
-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 example is a weak solution
-recognizes elliptic and parabolic partial differential equations and knows applicable existence, uniqueness and regularity results
-can employ regularity techniques for partial differential equations

Study methods

Returned exercises.

Content

Sobolev spaces and inequalities, weak derivatives, 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

Materials

Lecture note

Literature:

Assessment criteria for each grade

Grade is based on the exercise points as follows:
Grade 1: at least 50 %
Grade 2: at least 60 %
Grade 3: at least 70 %
Grade 4: at least 80 %
Grade 5: at least 90 %

Prerequisites

MATS230 Partial differential equations, MATS110 Measure and integration theory