Non-divergence equations structured on Hörmander vector fields : heat kernels and Harnack inequalities /

Saved in:
Bibliographic Details
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
Hidden Bibliographic Details
Other authors / contributors:Bramanti, Marco, 1963-
ISBN:9780821849033 (alk. paper)
0821849034 (alk. paper)
Notes:"Volume 204, number 961 (end of volume)."
Includes bibliographical references.
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