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Sobolev spaces (Summer Semester 2021)

Lecture: Tuesday 12:00-13:30 20.30 -01.11
Problem class: Thursday 18:00-19:30 20.30 -01.12
Lecturer PD Dr. Rainer Mandel
Office hours: by appointment
Room -1.019 Kollegiengebäude Mathematik (20.30)
Email: rainer.mandel@kit.edu
Problem classes Dr. Zoïs Moitier
Office hours: By appointment
Room -1.021 Kollegiengebäude Mathematik (20.30)
Email: zois.moitier@kit.edu

In this course we develop the theory of Sobolev spaces, which is indispensable for the modern theory of Partial Differential Equations. The main idea is to study functions with distributional derivatives given by L^p-functions and to take advantage of the theory of the associated Banach spaces, which are called Sobolev spaces. We will study the most important aspects of these spaces (Trace Theorems, Embedding Theorems) and demonstrate their usefulness in the context of the Calculus of Variations and basic elliptic Partial Differential Equations.

Prerequisites: Calculus, Basics of Functional Analysis, interest in PDEs

Lecture Notes (20.07.2021, changes wrt earlier version in color)


Exercise sheets:


Brezis: Functional Analysis
Evans: Partial Differential Equations
Adams: Sobolev Spaces