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VOL. 44 | 2006 The $L^p$ resolvents for elliptic systems of divergence form
Yoichi Miyazaki

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

## Abstract

We consider elliptic systems of divergence form in $\mathbb{R}^n$ under the limited smoothness assumptions on the coefficients. We construct $L^p$ resolvents with evaluation of their operator norms, and derive the Gaussian bounds for heat kernels and estimates for resolvent kernels. These results extend those for single operators.

## Information

Published: 1 January 2006
First available in Project Euclid: 16 December 2018

zbMATH: 1192.35044
MathSciNet: MR2277838

Digital Object Identifier: 10.2969/aspm/04410245

Subjects:
Primary: 31B10 , 35B20 , 35G05

Keywords: $L^p$ theory , elliptic system , heat kernel , non-smooth coefficients , Resolvent kernel