Speakers

Title: How much degeneracy causes non-smooth solutions for elliptic equations?

Speaker: Timur Akhunov (Wabash College)

Abstract: Solutions of the Laplace equation are always smooth in the interior of the domain. This property, shared with parabolic problems, is called hypoellipticity. This concept, introduced in 1940s led to substantial developments of PDE and probability techniques. Hypoellipticity can be present, if weaker, for non-uniformly (or degenerate) elliptic equations, for which the operator gives rise to a sub-Riemannian metric. In collaboration with Lyudmila Korobenko (Reed College) we investigate a threshold on degeneracy necessary for hypoellipticity.