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

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

Analysis of PDEs 2022-12-27 v1

Authors: Luciana Angiuli , Luca Lorenzi , Elisabetta M. Mangino

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.

Keywords

elliptic operators c0-semigroup vector-valued unbounded coefficients lebesgue space infinitesimal generator

Cite

@article{arxiv.2212.12784,
  title  = {Generation of semigroups associated to strongly coupled elliptic operator in $L^p(\mathbb R^d;\mathbb R^m)$},
  author = {Luciana Angiuli and Luca Lorenzi and Elisabetta M. Mangino},
  journal= {arXiv preprint arXiv:2212.12784},
  year   = {2022}
}

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