Differential and Integral Equations

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

Alessandra Lunardi and Giorgio Metafune

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J70: Degenerate elliptic equations
Secondary: 26D15: Inequalities for sums, series and integrals 35H10: Hypoelliptic equations 35K65: Degenerate parabolic equations 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 46F05: Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


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.

Export citation