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January/February 2014 Sharp constants for the $L^{\infty}$-norm on the torus and applications to dissipative partial differential equations
Michele V. Bartuccelli
Differential Integral Equations 27(1/2): 59-80 (January/February 2014).

Abstract

Sharp estimates are obtained for the constants appearing in the Sobolev embedding theorem for the $L^\infty$ norm on the $d-$dimensional torus for $d=1,2,3.$ The sharp constants are expressed in terms of the Riemann zeta-function, the Dirichlet beta-series and various lattice sums. We then provide some applications including the two dimensional Navier-Stokes equations.

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Michele V. Bartuccelli. "Sharp constants for the $L^{\infty}$-norm on the torus and applications to dissipative partial differential equations." Differential Integral Equations 27 (1/2) 59 - 80, January/February 2014.

Information

Published: January/February 2014
First available in Project Euclid: 12 November 2013

zbMATH: 1313.46043
MathSciNet: MR3161596

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Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 1/2 • January/February 2014
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