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Non-Divergence Equations Structured on Hörmander Vector Fields: Heat Kernels and Harnack Inequalities
 
Marco Bramanti Politecnico di Milano, Milan, Italy
Luca Brandolini Università di Bergamo, Bologna, Italy
Ermanno Lanconelli Università di Bologna, Bologna, Italy
Francesco Uguzzoni Università di Bologna, Bologna, Italy
Front Cover for Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
Available Formats:
Electronic ISBN: 978-1-4704-0575-5
Product Code: MEMO/204/961.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
Front Cover for Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
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  • Front Cover for Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
  • Back Cover for Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
Non-Divergence Equations Structured on Hörmander Vector Fields: Heat Kernels and Harnack Inequalities
Marco Bramanti Politecnico di Milano, Milan, Italy
Luca Brandolini Università di Bergamo, Bologna, Italy
Ermanno Lanconelli Università di Bologna, Bologna, Italy
Francesco Uguzzoni Università di Bologna, Bologna, Italy
Available Formats:
Electronic ISBN:  978-1-4704-0575-5
Product Code:  MEMO/204/961.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2042009; 123 pp
    MSC: 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
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Volume: 2042009; 123 pp
MSC: 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 \(T_{1} < T_{2}\).

  • 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
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