Fr'ed'eric Robert

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math.AP2025

Sharp multiscale control for high order nonlinear equations

Frédéric Robert

We analyze the behavior of families $(u_{α})_{α > 0}$ of solutions to the high-order critical equation $P_{α} u_{α} = Δ_{g}^{k} u_{α} + lot = ∣ u_{α} ∣^{2^{⋆} - 2} u_{α}$ on a Riemannian manifold $M$ ,…

math.AP2025

Optimal Sobolev inequalities of high order with $L^{2}$ -remainder

Lorenzo Carletti, Frédéric Robert

We investigate the validity of the optimal higher-order Sobolev inequality $H_{k}^{2} (M^{n}) ↪ L^{\frac{2 n}{n - 2 k}} (M^{n})$ on a closed Riemannian manifold when the remainder t…

math.AP2005

The Effect of Curvature on the Best Constatnt in the Hardy-Sobolev Inequalities

N. Ghoussoub, F. Robert

We address the question of attainability of the best constant in the following Hardy-Sobolev inequality on a smooth domain $Ω$ of \mathbb{R}^n: $$ μ_s (Ω) := \inf \{\int_Ω| \nabla…

Sharp multiscale control for high order nonlinear equations

Optimal Sobolev inequalities of high order with L2-remainder

The Effect of Curvature on the Best Constatnt in the Hardy-Sobolev Inequalities

Optimal Sobolev inequalities of high order with $L^{2}$ -remainder