Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs – Lectures 13-14, 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 )

1:00 pm - 2:15 pm

Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs – Lecture 13, Ugur Abdulla: Wiener criterion at infinity for the unique solvability of the Dirichlet problem in arbitrary open sets (Abdulla, 2007). Proof of the irregularity of infinity and non-uniqueness under the convergence of Wiener series at infinity.

2:15 pm - 2:45 pm
Tea / Coffee Break

2:45 pm - 4:00 pm

Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs – Lecture 14 (Active Learning Session), Ugur Abdulla: Wiener criterion at infinity for the unique solvability of the Dirichlet problem in arbitrary open sets (Abdulla, 2007). Proof of the regularity of infinity and uniqueness under the divergence of the Wiener series at infinity.