On a criterion for hypoellipticity

On global hypoellipticity

We consider a first order linear partial differential operator of principal type on a closed connected orientable two-dimensional manifold sending sections of one complex line bundle to sections of another. We prove that the assumption of global hypoellipticity of the operator implies a relation between the degrees of the line bundles and the Euler characteristic of the manifold.

On Hypoellipticity in G

A New Criterion for Screening Medical Applicants

Introduction. In the current screening system, new admissions are based on general intelligence as measured by universities entrance examination. Considering the fact that an important function of medical graduates is to educate the patients how to restore and take care of their health, communicative competence and skills would be, at least, as important as general intelligence. To show that la...

Hypoellipticity and Vanishing Theorems

Let −iLT (essentially Lie derivative with respect to T , a smooth nowhere zero real vector field) and P be commuting differential operators, respectively of orders 1 and m ≥ 1, the latter formally normal, both acting on sections of a vector bundle over a closed manifold. It is shown that if P + (−iLT ) m is elliptic then the restriction of −iLT to D ⊂ kerP ⊂ L (D is carefully specified) yields ...

Hypoellipticity in Infinite Dimensions

We consider semilinear parabolic stochastic PDEs driven by additive noise. The question addressed in this note is that of the regularity of transition probabilities. If the equation satisfies a Hörmander ‘bracket condition’, then any finite-dimensional projection of the solution has a smooth density with respect to Lebesgue measure. One key ingredient in the argument is a bound on ‘Wiener polyn...