Advanced Studies in Pure Mathematics

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

Yoichi Miyazaki

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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


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