Non-divergence equations structured on Hörmander vector fields : heat kernels and Harnack inequalities /
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| Imprint: | Providence, R.I. : American Mathematical Society, 2010. |
|---|---|
| Description: | vi, 123 p. : ill. ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; no. 961 Memoirs of the American Mathematical Society ; no. 961. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7936944 |
Table of Contents:
- Introduction
- Part I. Operators with constant coefficients: Overview of Part I
- Global extension of Hormander'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 Holder 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 Holder 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
