THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

University Homepage
DRPS Homepage
DRPS Search
DRPS Contact
DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Elliptic Partial Differential Equations (MATH10089)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThe aim of the course is to give an introduction to elliptic partial differential equations and their applications in geometry, material sciences, biology and finance. The student will learn about important concepts such as the notion of a weak solution, the maximum principle as well as important theoretical results, for example the Krylov-
Safonov theorem.
Course description Examples of elliptic PDEs and various types of weak solutions.
Weak differentiability, Sobolev spaces and classical solutions.
Harmonic functions: Mean value theorem, Greens function Poisson kernel.
Maximum principle for general linear equations.
Divergence form equations, Caccioppoli's inequality, Morrey's theorem in two dimensions.
Non-divergence form equations, strong and viscosity solutions.
Aleksandrov's maximum principle.
Krylov-Safonov's theorem.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068) OR Algebra and Calculus (PHYS08041) OR Linear Algebra and Several Variable Calculus (PHYS08042)
Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Not being delivered
Learning Outcomes
1. Reformulate equations of divergence form through integral identities using partial integration.
2. Evaluate or estimate the maximum and minimum of solutions of elliptic equation using the maximum principle.
3. Infer regularity of solutions from that of given data.
4. Explicitly compute the (radially) symmetric solutions and Green/Poisson kernels for the Laplace operator.
5. Estimate first and second order derivatives of solutions via integral norms of solution itself.
6. Compare qualitative properties of weak and viscosity solutions.
Reading List
Recommended :
E. Landis, Second Order Equations of Elliptic and Parabolic Type, AMS 1998
Qing Han, Fanghua Lin, Courant Institute Lecture notes, NYU, 2011
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 2011
Additional Information
Graduate Attributes and Skills Not entered
KeywordsEPDE
Contacts
Course organiserDr Martin Dindos
Tel:
Email: M.Dindos@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
Navigation
Help & Information
Home
Introduction
Glossary
Search DPTs and Courses
Regulations
Regulations
Degree Programmes
Introduction
Browse DPTs
Courses
Introduction
Humanities and Social Science
Science and Engineering
Medicine and Veterinary Medicine
Other Information
Combined Course Timetable
Prospectuses
Important Information
 
© Copyright 2015 The University of Edinburgh - 18 January 2016 4:24 am