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- W2949258393 abstract "We consider $(M,g)$ a smooth compact Riemannian manifold of dimension $n geq 2$ without boundary, $1 < p$ a real parameter and $r = frac{p(n + p)}{n}$. This paper concerns the validity of the optimal Moser inequality [ left(int_M |u|^r; dv_g right)^{frac{tau}{p}} leq left( A(p,n)^{frac{tau}{p}} left(int_M |nabla_g u|^p; dv_gright)^{frac{tau}{p}} + B_{opt} left(int_M |u|^p; dv_gright)^{frac{tau}{p}} right) left( int_M |u|^p; dv_g right)^{frac{tau}{n}} ; . ] This kind of inequality was already studied in the last years in the particular cases $1 < p < n$. Here we solve the case $n leq p$ and we introduce one more parameter $1 leq tau leq min{p,2}$. Moreover, we prove the existence of an extremal function for the optimal inequality above." @default.
- W2949258393 created "2019-06-27" @default.
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- W2949258393 date "2014-08-07" @default.
- W2949258393 modified "2023-09-27" @default.
- W2949258393 title "Sharp $L^p$-Moser inequality on Riemannian manifolds" @default.
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