L^p-quasicontractiveness and Kernel estimates for semigroups generated by systems of elliptic operators

L. Angiuli; E. M. Mangino; L. Lorenzi

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arXiv · 2510.07216

L^p-quasicontractiveness and Kernel estimates for semigroups generated by systems of elliptic operators

L. Angiuli·E. M. Mangino·L. Lorenzi

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Abstract

This paper focuses on systems of strongly coupled elliptic operators whose coefficients may be unbounded and are defined on a domain $\Omega \subseteq \mathbb{R}^d$. It is shown that a quasi-contractive semigroup in $L^p$-spaces can be associated with such operators for values of $p$ belonging to an interval that contains $2$ as an interior point. Then, under refined assumptions and considering systems of elliptic operators coupled up to first order, new kernel estimates are established with respect to a distance function that accounts for the growth of the diffusion coefficients and the potential term at infinity.

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L. Angiuli, E. M. Mangino, L. Lorenzi. 2025-10-08. L^p-quasicontractiveness and Kernel estimates for semigroups generated by systems of elliptic operators. https://arxiv.org/abs/2510.07216

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