## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Potential Theory in Matsue, H. Aikawa, T. Kumagai, Y. Mizuta and N. Suzuki, eds. (Tokyo: Mathematical Society of Japan, 2006), 245 - 254

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

#### 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

**Source***Potential Theory in Matsue*, H. Aikawa, T. Kumagai, Y. Mizuta and N. Suzuki, eds. (Tokyo: Mathematical Society of Japan, 2006), 245-254

**Dates**

Received: 31 March 2005

Revised: 28 July 2005

First available in Project Euclid:
16 December 2018

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.2969/aspm/04410245

**Mathematical Reviews number (MathSciNet)**

MR2277838

**Zentralblatt MATH identifier**

1192.35044

**Subjects**

Primary: 35G05: Linear higher-order equations 35B20: Perturbations 31B10: Integral representations, integral operators, integral equations methods

**Keywords**

elliptic system $L^p$ theory non-smooth coefficients heat kernel resolvent kernel

#### 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