Elliptic operators with unbounded diffusion coefficients in Lp spaces

TL;DR

This paper investigates elliptic operators with unbounded diffusion coefficients in Lp spaces, establishing conditions for their semigroup generation, domain characterization, and spectral properties.

Contribution

It provides new results on the generation of contraction and analytic semigroups for operators with unbounded coefficients and characterizes their domains and spectra.

Findings

Operators generate contraction or analytic semigroups in Lp

Explicit domain descriptions for certain parameter ranges

Spectral properties and composition insights

Abstract

In this paper we prove that, under suitable assumptions on {\alpha} > 0, the operator L = (1 + |x|{\alpha})\Delta admits realizations generating contraction or analytic semigroups in Lp (RN). For some values of {\alpha}, we also explicitly characterize the domain of L. Finally, some informations about the location and composition of the spectrum are given.