## Advanced Studies in Pure Mathematics

### The $L^p$ resolvents for elliptic systems of divergence form

Yoichi Miyazaki

#### 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.

#### Article information

Dates
Revised: 28 July 2005
First available in Project Euclid: 16 December 2018

https://projecteuclid.org/ euclid.aspm/1544999695

Digital Object Identifier
doi:10.2969/aspm/04410245

Mathematical Reviews number (MathSciNet)
MR2277838

Zentralblatt MATH identifier
1192.35044

#### Citation

Miyazaki, Yoichi. The $L^p$ resolvents for elliptic systems of divergence form. Potential Theory in Matsue, 245--254, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04410245. https://projecteuclid.org/euclid.aspm/1544999695