Abstract.
By a method of cylindrical symmetrization for the functions belonging to \( C^\infty_c ({\Bbb R}^{n-1} \times [0,+\infty[) \), we give an estimate of the best constant in the trace Nash inequality on \( {\Bbb R}^{n-1} \times [0,+\infty[ \). Then, we adapt this result on compact Riemannian manifolds with boundary.
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Submitted: January 2000, Revised version: April 2000.
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Humbert, E. Optimal trace Nash inequality . GAFA, Geom. funct. anal. 11, 759–772 (2001). https://doi.org/10.1007/PL00001684
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DOI: https://doi.org/10.1007/PL00001684