Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$- and $C_b$-spaces

Abstract

Let $a$ and $b$ be unbounded functions in $\mathbb R^N$ with $a$sufficiently smooth. In this paper we prove that, under suitablegrowth assumptions on $a$ and $b$, the operator $Au=a\Delta u+b\cdot\nabla u$ admits realizations generatinganalytic semigroups in $L^p( R^N)$ for any $p\in[1,+\infty]$ and in $C_b( R^N)$. We also explicitlycharacterize the domain of the infinitesimal generator of suchsemigroups. Similar results are stated and proved when $R^N$ is replaced with a smooth exterior domain under general boundaryconditions.

Locations

• Discrete and Continuous Dynamical Systems - View
• INFM-OAR (INFN Catania) - View - PDF