# 101.631 AKANA An Introduction to Viscosity Solutions of Fully Nonlinear 2nd Order PDE Diese Lehrveranstaltung ist in allen zugeordneten Curricula Teil der STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});Diese Lehrveranstaltung ist in mindestens einem zugeordneten Curriculum Teil der STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2016S

2016S, VO, 2.0h, 3.0EC

## Merkmale

• Semesterwochenstunden: 2.0
• ECTS: 3.0
• Typ: VO Vorlesung

## Ziele der Lehrveranstaltung

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¿.

## Inhalt der Lehrveranstaltung

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

## Weitere Informationen

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

## LVA Termine

TagZeitDatumOrtBeschreibung
Mo.15:00 - 17:0002.05.2016 - 09.05.2016Sem.R. DA grün 06B Prof. Katzourakis
Mi.16:00 - 18:0004.05.2016 - 18.05.2016Sem.R. DA grün 03 C Prof. Katzourakis
Fr.14:00 - 17:0006.05.2016 - 20.05.2016Sem.R. DA grün 03 C Prof. Katzourakis
Mo.15:00 - 17:0016.05.2016Sem.R. DA grün 03 C Prof. Katzourakis
Mo.15:00 - 16:0023.05.2016Sem.R. DA grün 06B Prof. Katzourakis
Di.14:00 - 16:0024.05.2016Sem.R. DA grün 06B Prof. Katzourakis Prüfungen
AKANA An Introduction to Viscosity Solutions of Fully Nonlinear 2nd Order PDE - Einzeltermine
TagDatumZeitOrtBeschreibung
Mo.02.05.201615:00 - 17:00Sem.R. DA grün 06B Prof. Katzourakis
Mi.04.05.201616:00 - 18:00Sem.R. DA grün 03 C Prof. Katzourakis
Fr.06.05.201614:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mo.09.05.201615:00 - 17:00Sem.R. DA grün 06B Prof. Katzourakis
Mi.11.05.201616:00 - 18:00Sem.R. DA grün 03 C Prof. Katzourakis
Fr.13.05.201614:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mo.16.05.201615:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mi.18.05.201616:00 - 18:00Sem.R. DA grün 03 C Prof. Katzourakis
Fr.20.05.201614:00 - 17:00Sem.R. DA grün 03 C Prof. Katzourakis
Mo.23.05.201615:00 - 16:00Sem.R. DA grün 06B Prof. Katzourakis
Di.24.05.201614:00 - 16:00Sem.R. DA grün 06B Prof. Katzourakis Prüfungen

mündl.

## LVA-Anmeldung

Nicht erforderlich

## Curricula

StudienkennzahlSemesterAnm.Bed.Info
860 GW Gebundene Wahlfächer - Technische Mathematik

## Literatur

Es wird kein Skriptum zur Lehrveranstaltung angeboten.

Englisch