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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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