# Module for [Scientific Computing]

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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 | - HÃ¶lder continuity of weak solutions of linear partial differential equations: Sobolev spaces, Harnack inequality, De GiorgiâNash theory, Moserâs iteration technique. - HÃ¶lder continuity of the gradient of a solution: Application of the De GiorigiâNash estimates to the gradient of the solution of an elliptic quasilinear differential equation, Morreyâs lemma. - Existence theory for quasilinear elliptic differential equations: Continuity method, fixed point theorems, Leray-Schauderâs 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 |