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.
Citation
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. https://doi.org/10.57262/die/1384282854
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