Difference between revisions of "Math 647: Theory of Partial Differential Equations 1"

Revision as of 13:26, 4 June 2009

Theory of Partial Differential Equations 1.

3

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

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 === Title ===
-Theory of Partial Differential Equations.
+Theory of Partial Differential Equations 1.
 === Credit Hours ===
@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 347]], [[Math 542|542]].
+[[Math 541]], [[Math 547|547]].
 === Description ===