About: Gagliardo–Nirenberg interpolation inequality

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In mathematics, and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates the -norms of different weak derivatives of a function through an interpolation inequality. The theorem is of particular importance in the framework of elliptic partial differential equations and was originally formulated by Emilio Gagliardo and Louis Nirenberg in 1958. The Gagliardo-Nirenberg inequality has found numerous applications in the investigation of nonlinear partial differential equations, and has been generalized to fractional Sobolev spaces by Haim Brezis and in the late 2010s.

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  • In mathematics, and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates the -norms of different weak derivatives of a function through an interpolation inequality. The theorem is of particular importance in the framework of elliptic partial differential equations and was originally formulated by Emilio Gagliardo and Louis Nirenberg in 1958. The Gagliardo-Nirenberg inequality has found numerous applications in the investigation of nonlinear partial differential equations, and has been generalized to fractional Sobolev spaces by Haim Brezis and in the late 2010s. (en)
  • En mathématiques, l'inégalité de Gagliardo-Nirenberg est une estimation portant sur les dérivées faibles d'une fonction donnée. Elle fait intervenir les normes de la fonction ainsi que ses dérivées. C'est un résultat particulièrement important de la théorie des équations aux dérivées partielles. Cette inégalité a été proposée par Louis Nirenberg et . (fr)
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  • 1119661814 (xsd:integer)
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  • Let be a measurable, bounded, open and connected domain satisfying the cone condition. Let be a positive extended real quantity. Let and be non-negative integers such that . Furthermore, let be a positive extended real quantity, be real and such that the relations hold. Then, where such that and is arbitrary, with one exceptional case: # if and is a non-negative integer, then the additional assumption is needed. In any case, the constant depends on the parameters , on the domain , but not on . (en)
  • Let be a positive extended real quantity. Let and be non-negative integers such that . Furthermore, let be a positive extended real quantity, be real and such that the relations hold. Then, for any such that , with two exceptional cases: # if , and , then an additional assumption is needed: either tends to 0 at infinity, or for some finite value of ; # if and is a non-negative integer, then the additional assumption is needed. In any case, the constant depends on the parameters , but not on . (en)
  • Let be either the whole space, a half-space or a bounded Lipschitz domain. Let be three positive extended real quantities and let be non-negative real numbers. Furthermore, let and assume that hold. Then, for any if and only if The constant depends on the parameters , on the domain , but not on . (en)
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  • Theorem (en)
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  • Brezis-Mironescu (en)
  • Gagliardo-Nirenberg (en)
  • Gagliardo-Nirenberg in bounded domains (en)
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  • In mathematics, and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates the -norms of different weak derivatives of a function through an interpolation inequality. The theorem is of particular importance in the framework of elliptic partial differential equations and was originally formulated by Emilio Gagliardo and Louis Nirenberg in 1958. The Gagliardo-Nirenberg inequality has found numerous applications in the investigation of nonlinear partial differential equations, and has been generalized to fractional Sobolev spaces by Haim Brezis and in the late 2010s. (en)
  • En mathématiques, l'inégalité de Gagliardo-Nirenberg est une estimation portant sur les dérivées faibles d'une fonction donnée. Elle fait intervenir les normes de la fonction ainsi que ses dérivées. C'est un résultat particulièrement important de la théorie des équations aux dérivées partielles. Cette inégalité a été proposée par Louis Nirenberg et . (fr)
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  • Inégalité d'interpolation de Gagliardo-Nirenberg (fr)
  • Gagliardo–Nirenberg interpolation inequality (en)
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