The \(L^p\) resolvents for elliptic systems of divergence form. (English) Zbl 1192.35044

Aikawa, Hiroaki (ed.) et al., Potential theory in Matsue. Selected papers of the international workshop on potential theory, Matsue, Japan, August 23–28, 2004. Tokyo: Mathematical Society of Japan (ISBN 4-931469-33-7/hbk). Advanced Studies in Pure Mathematics 44, 245-254 (2006).
Summary: 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.
For the entire collection see [Zbl 1102.31001].


35J48 Higher-order elliptic systems
35B20 Perturbations in context of PDEs
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
47G30 Pseudodifferential operators
47A10 Spectrum, resolvent