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2004 On the domains of elliptic operators in $L^1$
Alessandra Lunardi, Giorgio Metafune
Differential Integral Equations 17(1-2): 73-97 (2004).

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.

Citation

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Alessandra Lunardi. Giorgio Metafune. "On the domains of elliptic operators in $L^1$." Differential Integral Equations 17 (1-2) 73 - 97, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1164.35365
MathSciNet: MR2035496

Subjects:
Primary: 35J70
Secondary: 26D15 , 35H10 , 35K65 , 46E35 , 46F05 , 47D06

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 1-2 • 2004
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