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	Título: Non-Divergence Equations Structured On Hörmander Vector Fields. Heat Kernels And
	Autor: Bramanti Marco/ Brandolini Luca/ Lanconelli Ermanno/ Uguzzon	Precio: $873.36
	Editorial: American Mathematical Society	Año: 2009
	Tema: Matematicas, Textos, Teorias	Edición: 1ª
	Sinopsis	ISBN: 9780821849033
	In this work the authors deal with 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 Hörmander'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} < T_{2}. Table of Contents Introduction Part I: Operators with constant coefficients Overview of Part I Global extension of Hörmander's vector fields and geometric properties of the CC-distance Global extension of the operator H_{A} and existence of a fundamental solution Uniform Gevray estimates and upper bounds of fundamental solutions for large d\left(x,y\right) Fractional integrals and uniform L^{2} bounds of fundamental solutions for large d\left(x,y\right) Uniform global upper bounds for fundamental solutions Uniform lower bounds for fundamental solutions Uniform upper bounds for the derivatives of the fundamental solutions Uniform upper bounds on the difference of the fundamental solutions of two operators Part II: Fundamental solution for operators with Hölder continuous coefficients Assumptions, main results and overview of Part II Fundamental solution for H: the Levi method The Cauchy problem Lower bounds for fundamental solutions Regularity results Part III: Harnack inequality for operators with Hölder continuous coefficients Overview of Part III Green function for operators with smooth coefficients on regular domains Harnack inequality for operators with smooth coefficients Harnack inequality in the non-smooth case Epilogue References

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