Department of Mathematics

Analysis and PDE

  •  Farhan Abedin, Michigan State University
  •  Regularity results for a class of Kolmogorov-Fokker-Planck equations in non-divergence form
  •  11/13/2019
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

The Kolmogorov-Fokker-Planck equation is a degenerate parabolic equation arising in models of gas dynamics from kinetic theory. The operator is of the form $$\mathcal{L}_Au := \mathrm{tr}(A(v,y,t) D^2_v u) + v \cdot \nabla_yu - \partial_tu,$$ where $$u(v,y,t): \mathbb{R}^{2d+1} \to \mathbb{R} \text{ and } 0 < \lambda \mathbb{I}_d \leq A \leq \Lambda \mathbb{I}_d.$$ It is an open problem if non-negative solutions of $\mathcal{L}_A u = 0$ in $\mathbb{R}^{2d+1}$ satisfy a scale-invariant Harnack inequality, assuming the matrix coefficient $A$ is merely bounded and measurable. I will discuss recent joint work with Giulio Tralli in which progress is made on partially solving this problem.

 

Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science