Ruprecht-Karls-Universität Heidelberg
Siegel der Universität Heidelberg

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[Partial Differential Equations II] - [2015 Sommer]

Module Code
MH03
Name
Partial Differential Equations II
Credit Points
8 CP
Workload
240
Duration
1 semester
Cycle
0
Methods Lecture 4 h + Exercise course 2 h
Objectives To have a firm command of the existence and regularity theories for solutions of nonlinear partial differential equations of second order.
Content - Hölder continuity of weak solutions of linear partial differential equations: Sobolev spaces, Harnack inequality, De Giorgi–Nash theory, Moser’s iteration technique. - Hölder continuity of the gradient of a solution: Application of the De Giorigi–Nash estimates to the gradient of the solution of an elliptic quasilinear differential equation, Morrey’s lemma. - Existence theory for quasilinear elliptic differential equations: Continuity method, fixed point theorems, Leray-Schauder’s fixed point theorem.
Learning outcomes The capability of solving problems in the underlying field. The capability to present the solutions in the exercise courses.
Prerequisites
Suggested previous knowledge Partial Differential Equations I, Schauder theory.
Assessments Homework consisting of solving exercises and a written or oral examination at the end of the term.
Literature David Gilbarg, Neal Trudinger: Elliptic partial differential equations of second order
R.A. Adams: Sobolev spaces
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