Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs – Lectures 1-2, Ugur Abdulla

2nd OIST-Oxford-SLMath Summer Graduate School on Analysis and Partial Differential Equations

Course II: Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs (Ugur Abdulla )

9:00 am - 10:15 am

Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs – Lecture 1, Ugur Abdulla, Harmonic functions - the mathematical representation of physical quantities in equilibrium; fundamental harmonic function; representation formula for the gravitational potential via Poisson's PDE.

10:30 am - 11:45 am

Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs – Lecture 2 (Active Learning Session), Ugur Abdulla, Mean value formulas, maximum/minimum principle for smooth sub-/superharmonic functions; uniqueness of the solution to the Dirichlet problem in bounded open sets;