A parametrix for step-two hypoelliptic diffusion equations. (English) Zbl 0602.35021
The author constructs a parametrix for the hypoelliptic diffusion equations \((\partial /\partial t-L)u=0\) where \(L=\sum^{n}_{\alpha =1}x^ 2_{\alpha}\) and where the \(x_{\alpha}\) are vector fields which satisfy the property that they together with all of the commutators \([x_{\alpha},x_{\beta}]\) for \(\alpha <\beta\), are at each point linearly independent and span the tangent space.
Reviewer: C.Zuily
MSC:
| 35H10 | Hypoelliptic equations |
| 35K65 | Degenerate parabolic equations |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
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