Generation of semigroups associated to strongly coupled elliptic operator in $L^p(\mathbb R^d;\mathbb R^m)$

Luciana Angiuli; Luca Lorenzi; Elisabetta M. Mangino

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arXiv · 2212.12784

Generation of semigroups associated to strongly coupled elliptic operator in $L^p(\mathbb R^d;\mathbb R^m)$

Luciana Angiuli·Luca Lorenzi·Elisabetta M. Mangino

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Abstract

A class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space $L^p(\mathbb R^d;\mathbb R^m)$ with $p \in (1,\infty)$, providing sufficient conditions for the generation of an analytic $C_0$-semigroup $T(t)$. Under further assumptions, a characterization of the domain of the infinitesimal generator is given.

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Luciana Angiuli, Luca Lorenzi, Elisabetta M. Mangino. 2022-12-24. Generation of semigroups associated to strongly coupled elliptic operator in $L^p(\mathbb R^d;\mathbb R^m)$. https://arxiv.org/abs/2212.12784

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