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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
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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 Click above image for expanded view 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 $T_{1} < T_{2}$.

• 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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