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- W2273162584 abstract "Let (M,g) be a smooth compact Riemannian manifold of dimension n geq 2, 1 < p < n and 1 leq q < r < p^ast = frac{np}{n-p} be real parameters. This paper concerns to the validity of the optimal Gagliardo-Nirenberg inequality (int_M |u|^r; dv_g)^{frac{tau}{r theta}} leq (A_{opt} (int_M |nabla_g u|^p; dv_g)^{frac{tau}{p}} + B_{opt} (int_M |u|^p; dv_g)^{frac{tau}{p}}) (int_M |u|^q; dv_g)^{frac{tau(1 - theta)}{theta q}} ; . This kind of inequality is studied in Chen and Sun (Nonlinear Analysis 72 (2010), pp. 3159-3172) where the authors established its validity when 2 < p < r < p^ast and (implicitly) tau = 2. Here we solve the case p geq r and introduce one more parameter 1 leq tau leq min{p,2}. Moreover, we prove the existence of extremal function for the optimal inequality above." @default.
- W2273162584 created "2016-06-24" @default.
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- W2273162584 date "2016-01-01" @default.
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- W2273162584 title "Sharp constants in RiemannianLp-Gagliardo–Nirenberg inequalities" @default.
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- W2273162584 doi "https://doi.org/10.1016/j.jmaa.2015.07.023" @default.
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