Modules

Prerequisites

Contents

On the functional analytic basis, the classical and weak solution theories for linear elliptic differential equations in n variables shall be treated within this lecture. From the lecture notes below, the following themes will be discussed: Potential theoretic foundations, Dirichlet's problem for the Laplace equation and Perron's method, Schauder's continuity method and the Dirichlet problem in Hölder spaces, Existence of weak solutions and their regularity, Moser's iteration method, Green's function for elliptic differential operators.

Learning outcomes

After successfully completing the module, students have deeper knowledge on Analysis and Complex Analysis. They are familiar with the most important concepts and interrelations of partial differential equations and have competently mastered the various analytic methods to solve partial differential equations. Using topics on partial differential equations as examples, students have gained experience in independent scientific work.

Assessment

Prerequisite: • Successful completion of homework Final module examination: • Written examination, 90 min. OR • Oral examination, 30 min. It will be announced in the first class whether the examination will organized in written or oral form.

Remarks

• Study programme Mathematics M.Sc.: Compulsory elective module in complex „Analysis/Algebra/Combinatorics“ • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend • Study programme Physik B.Sc.: Compulsory elective module in complex „Nebenfach“