Sobolev estimates for parabolic and elliptic equations with uniformly degenerate coefficients

Hongjie Dong (Brown U, Providence)

Feb 24. 2025, 11:00 — 11:50

We study a class of degenerate parabolic and elliptic equations in the upper half space $\{x_d>0\}$. The leading coefficients are of the form $x_d^2a_{ij}$, where $a_{ij}$ are measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. Additionally, they have small bounded mean oscillations in the other spatial variables. We obtain the well-posedness and regularity of solutions in weighted mixed-norm Sobolev spaces.

Based on joint work with Junhee Ryu.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Degenerate and Singular PDEs (Workshop)
Organizer(s):
Verena Bögelein (PLUS, Salzburg)
Ugo Gianazza (U of Pavia)
Juha Kinnunen (Aalto U)
Naian Liao (PLUS, Salzburg)