6 problems

Hypoellipticity characterization. The operator $L$ is locally $C^\infty$-hypoelliptic if and only if both $L_1$ and $L_2$ satisfy the superlogarithmic estimate.

Let $P(D)$ be a hypoelliptic partial differential operator on $\mathbb{R}^d$ which is orthogonally degenerate on its linear characteristic cone … Moreover, let $F_1\subset F_2$ be…

Hypoelliptic damping conjecture. The second part of the theorem for the elliptically perturbed operator $P_\epsilon$ holds with $\widetilde P_\epsilon$ in place of $P_\epsilon$. Th…

Let $P(\Delta)$ be an operator on a product of p.c.f. fractals, and let $P_0$ be the principal part of $P$. The operator is quasielliptic if there is a constant $c>0$ such that … f…

Let $P$ be a polynomial in $m$ variables and let $P(\Delta)$ be the corresponding operator on a product of p.c.f. fractals. For a multi-index $\kappa$, write $D^{\kappa}P$ for the…

Let $X$ be a p.c.f. fractal, let $P$ be a polynomial, and let $P(\Delta)$ denote the associated operator on the product space $X^m$. The operator $P(\Delta)$ is elliptic when…