Difference between revisions of "Math 647: Theory of Partial Differential Equations 1"
From MathWiki
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=== Title === | === Title === | ||
+ | Theory of Partial Differential Equations. | ||
− | === | + | === Credit Hours === |
− | + | 3 | |
− | + | ||
=== Prerequisite === | === Prerequisite === | ||
+ | [[Math 347]], [[Math 542|542]]. | ||
=== Description === | === Description === | ||
− | |||
− | |||
== Chris Grant's Proposed Core Topics for Math 647/648 == | == Chris Grant's Proposed Core Topics for Math 647/648 == |
Revision as of 12:22, 9 May 2008
Contents
Catalog Information
Title
Theory of Partial Differential Equations.
Credit Hours
3
Prerequisite
Description
Chris Grant's Proposed Core Topics for Math 647/648
- Linear elliptic operators of order n
- Classification
- Strong and weak solutions
- Gårding's inequality
- Existence of weak solutions for the Dirichlet and Neumann problems
- Agmon-Douglis-Nirenberg regularity
- Green's formula
- Fundamental solutions for general linear differential operators
- Green's functions for general linear BVPs
- Dirichlet's Principle for Laplace’s equation in Rn
- Poisson's Equation
- Newtonian Potential
- Local existence for the Dirichlet Problem with locally Hölder boundary data
- Interior Hölder estimates
- Kellogg's Theorem
- Second-order linear elliptic operators
- Weak Maximum Principle
- Perron's Method
- Uniqueness for the Dirichlet Problem
- Hopf's bondary-point lemma
- Hopf's Strong Maximum Principle
- Alexandroff Maximum Principle
- Gidas-Ni-Nirenberg
- Uniqueness for the Neumann Problem
- Harnack inequality
- Finite difference methods
- Interior regularity
- Schauder estimates
- Moser iteration
- De Giorgi's theorem
- Boundary/Global regularity
- Second-order quasilinear equations in divergence form
- Existence of weak solutions for the Dirichlet problem via the Browder-Minty theorem
- Local-in-time existence for reaction-diffusion IBVPs and systems using the contraction mapping principle
- Abstract evolution equations
- General theory
- Existence and reqularity for parabolic IVPs
- Existence for hyperbolic IVPs
- Viscosity solutions