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Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
Marco Bramanti
其他書名
Heat Kernels and Harnack Inequalities
出版American Mathematical Soc., 2010
主題Mathematics / GeneralMathematics / Differential Equations / GeneralMathematics / Vector AnalysisMathematics / Functional Analysis
ISBN08218490349780821849033
URLhttp://books.google.com.hk/books?id=PQbDCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Examines linear second order partial differential operators of the following type $H=\partial_{t}-L=\partial_{t}-\sum_{i,j=1}^{q}a_{ij}(t,x) X_{i}X_{j}-\sum_{k=1}^{q}a_{k}(t,x)X_{k}-a_{0}(t,x)$ where $X_{1},X_{2},\ldots,X_{q}$ is a system of real Hormander's vector fields in some bounded domain $\Omega\subseteq\mathbb{R}^{n}$, $A=\left\{ a_{ij}\left( t,x\right) \right\} _{i,j=1}^{q}$ is a real symmetric uniformly positive definite matrix such that $\lambda^{-1}\vert\xi\vert^{2}\leq\sum_{i,j=1}^{q}a_{ij}(t,x) \xi_{i}\xi_{j}\leq\lambda\vert\xi\vert^{2}\text{}\forall\xi\in\mathbb{R}^{q}, x \in\Omega,t\in(T_{1},T_{2})$ for a suitable constant $\lambda>0$ a for some real numbers $T_{1}