## Differential and Integral Equations

### On the domains of elliptic operators in $L^1$

#### Abstract

We prove optimal embedding estimates for the domains of second-order elliptic operators in $L^1$ spaces. Our procedure relies on general semigroup theory and interpolation arguments, and on estimates for $\nabla T(t)f$ in $L^1$, in $L^\infty$, and possibly in fractional Sobolev spaces, for $f\in L^1$. It is applied to a number of examples, including some degenerate hypoelliptic operators, and operators with unbounded coefficients.

#### Article information

Source
Differential Integral Equations Volume 17, Number 1-2 (2004), 73-97.

Dates
First available in Project Euclid: 21 December 2012

Lunardi, Alessandra; Metafune, Giorgio. On the domains of elliptic operators in $L^1$. Differential Integral Equations 17 (2004), no. 1-2, 73--97.https://projecteuclid.org/euclid.die/1356060473