Differential and Integral Equations

Garding inequality on unbounded domains

Senoussi Guesmia

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This note presents a simple method to generalize the Garding inequality to unbounded domains. By introducing a special partition of unity associated to some covering of unbounded domains, we show that the Garding inequality, known in the literature on bounded domains (see Garding, 1953), holds for more general domains. The method proposed here only requires weak smoothness assumptions which allows coverage of a large class of elliptic operators. It also gives a new tool to extend some local properties to global ones, in particular when we deal with functions vanishing on the boundary.

Article information

Differential Integral Equations, Volume 23, Number 11/12 (2010), 1091-1103.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A30: Norms (inequalities, more than one norm, etc.) 35J30: Higher-order elliptic equations [See also 31A30, 31B30]


Guesmia, Senoussi. Garding inequality on unbounded domains. Differential Integral Equations 23 (2010), no. 11/12, 1091--1103. https://projecteuclid.org/euclid.die/1356019074

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