## Fundamental solutions for second order subelliptic operators.(English)Zbl 0613.35002

This paper deals with the fundamental solution of a second-order linear partial differential operator L on a compact manifold M with smooth measure $$\mu$$. In local coordinates $L=- \sum^{n}_{i,j=1}a^{ij}(x)\partial x_ i\partial x_ j+\sum^{n}_{k=1}b^ k(x)\partial x_ k+c(x),$ where $$(a^{ij})$$, $$(b^ k)$$, c are real, $$n>2$$, the matrix $$(a^{ij}(x))$$ is positive semidefinite, and L is subelliptic.
The author investigates the behavior of the fundamental solution G(x,y) near $$x=y$$ and finds out its estimates. Furthermore, the author gets some new estimates for solution of the equation $$Lu=f$$.
Reviewer: Z.Xu

### MSC:

 35A08 Fundamental solutions to PDEs 35G05 Linear higher-order PDEs 47F05 General theory of partial differential operators 58J99 Partial differential equations on manifolds; differential operators
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