4. November 2026
Daniel Tietz (Okinawa Institute of Science and Technology)
Kolmogorov-Petrovsky-type criterion for the removability of the fundamental singularity for divergence form parabolic PDEs
We study the singular Dirichlet problem for a general divergence form parabolic operator with the goal of establishing a necessary and sufficient condition for the unique solvability expressed in terms of a Kolmogorov-Petrovsky-type criterion for the removability of the fundamental singularity.
To this end, we use the concepts of h-Perron solution and suitable asymptotic properties of the fundamental solution. The result builds on the recent work for the removability of the fundamental singularity for the heat equation [Abdulla, 2024], and a previous work of [Garofalo, Lanconelli, 1989], where the asymptotic expansion of the fundamental solution for the linear second-order divergence form parabolic operators is established.
This is a joint work with Prof. Dr. Ugur G. Abdulla.