Electronic ISBN:  9781470405755 
Product Code:  MEMO/204/961.E 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $43.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 204; 2009; 123 ppMSC: Primary 35;
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 \[\lambda^{1}\vert\xi\vert^{2}\leq\sum_{i,j=1}^{q}a_{ij}(t,x) \xi_{i}\xi_{j}\leq\lambda\vert\xi\vert^{2}\forall\xi\in\mathbb{R}^{q}, x \in\Omega,t\in(T_{1},T_{2})\] for a suitable constant \(\lambda>0\) a for some real numbers \(T_{1} < T_{2}\).

Table of Contents

Chapters

Introduction

Part I: Operators with constant coefficients

Part II: Fundamental solution for operators with Hölder continuous coefficients

Part III: Harnack inequality for operators with Hölder continuous coefficients

Epilogue


RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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 \[\lambda^{1}\vert\xi\vert^{2}\leq\sum_{i,j=1}^{q}a_{ij}(t,x) \xi_{i}\xi_{j}\leq\lambda\vert\xi\vert^{2}\forall\xi\in\mathbb{R}^{q}, x \in\Omega,t\in(T_{1},T_{2})\] for a suitable constant \(\lambda>0\) a for some real numbers \(T_{1} < T_{2}\).

Chapters

Introduction

Part I: Operators with constant coefficients

Part II: Fundamental solution for operators with Hölder continuous coefficients

Part III: Harnack inequality for operators with Hölder continuous coefficients

Epilogue