101.631 AKANA An Introduction to Viscosity Solutions of Fully Nonlinear 2nd Order PDE
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2016S, VO, 2.0h, 3.0EC

Properties

  • Semester hours: 2.0
  • Credits: 3.0
  • Type: VO Lecture

Aim of course

The purpose of these lectures is to give a quick and elementary, yet rigorous, presentation of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are nonsmooth and standard approaches in order to define a ¿weak solution¿ do not apply because the standard idea of using ¿integration-by-parts¿ in order to pass derivatives to smooth test functions by duality, is not available. After developing some main theory, we will focus on applications in the modern field of Calculus of Variations in L¿.

 

Subject of course

Part I General Theory

- History, Examples, Motivation and First Definitions

- Second Definitions and Basic Analytic Properties of the Notions

- Stability Properties of the Notions and Existence via Approximation

-  Mollification of Viscosity Solutions and Semiconvexity

- Existence of Solution to the Dirichlet Problem via Perron's Method

-Comparison results and Uniqueness of Solution to the Dirichlet Problem

 

Part II Applications

- Minimisers of Convex Functionals and Viscosity Solutions of the Euler-Lagrange PDE

Existence of Viscosity Solutions to the Dirichlet Problem for the ¿Laplacian

 

Additional information

The course will be held by Prof. Dr. Nicos Katzourakis, Department of Mathematics and Statistics, University of Reading

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Mon15:00 - 17:0002.05.2016 - 09.05.2016Sem.R. DA grün 06B Prof. Katzourakis
Wed16:00 - 18:0004.05.2016 - 18.05.2016Sem.R. DA grün 03 C Prof. Katzourakis
Fri14:00 - 17:0006.05.2016 - 20.05.2016Sem.R. DA grün 03 C Prof. Katzourakis
Mon15:00 - 17:0016.05.2016Sem.R. DA grün 03 C Prof. Katzourakis
Mon15:00 - 16:0023.05.2016Sem.R. DA grün 06B Prof. Katzourakis
Tue14:00 - 16:0024.05.2016Sem.R. DA grün 06B Prof. Katzourakis exams
AKANA An Introduction to Viscosity Solutions of Fully Nonlinear 2nd Order PDE - Single appointments
DayDateTimeLocationDescription
Mon02.05.201615:00 - 17:00Sem.R. DA grün 06B Prof. Katzourakis
Wed04.05.201616:00 - 18:00Sem.R. DA grün 03 C Prof. Katzourakis
Fri06.05.201614:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mon09.05.201615:00 - 17:00Sem.R. DA grün 06B Prof. Katzourakis
Wed11.05.201616:00 - 18:00Sem.R. DA grün 03 C Prof. Katzourakis
Fri13.05.201614:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mon16.05.201615:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Wed18.05.201616:00 - 18:00Sem.R. DA grün 03 C Prof. Katzourakis
Fri20.05.201614:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mon23.05.201615:00 - 16:00Sem.R. DA grün 06B Prof. Katzourakis
Tue24.05.201614:00 - 16:00Sem.R. DA grün 06B Prof. Katzourakis exams

Examination modalities

oral

Course registration

Not necessary

Curricula

Literature

No lecture notes are available.

Language

English