Fefferman, Charles L.; Sánchez-Calle, Antonio Fundamental solutions for second order subelliptic operators. (English) Zbl 0613.35002 Ann. Math. (2) 124, 247-272 (1986). 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 Cited in 3 ReviewsCited in 60 Documents 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 Keywords:fundamental solution; compact manifold; smooth measure; subelliptic; estimates PDFBibTeX XMLCite \textit{C. L. Fefferman} and \textit{A. Sánchez-Calle}, Ann. Math. (2) 124, 247--272 (1986; Zbl 0613.35002) Full Text: DOI