[HTML][HTML] Equivalence of optimal L1-inequalities on Riemannian Manifolds
J Ceccon, L Cioletti - Journal of Mathematical Analysis and Applications, 2015 - Elsevier
J Ceccon, L Cioletti
Journal of Mathematical Analysis and Applications, 2015•ElsevierLet (M, g) be a smooth compact Riemannian manifold of dimension n≥ 2. This paper
concerns the validity of the optimal Riemannian L 1-Entropy inequality Ent dvg (u)≤ n
log(A opt‖ D u‖ BV (M)+ B opt) for all u∈ BV (M) with‖ u‖ L 1 (M)= 1 and existence of
extremal functions. In particular, we prove that this optimal inequality is equivalent to an
optimal L 1-Sobolev inequality obtained by Druet [3].
concerns the validity of the optimal Riemannian L 1-Entropy inequality Ent dvg (u)≤ n
log(A opt‖ D u‖ BV (M)+ B opt) for all u∈ BV (M) with‖ u‖ L 1 (M)= 1 and existence of
extremal functions. In particular, we prove that this optimal inequality is equivalent to an
optimal L 1-Sobolev inequality obtained by Druet [3].
Let (M, g) be a smooth compact Riemannian manifold of dimension n≥ 2. This paper concerns the validity of the optimal Riemannian L 1-Entropy inequality Ent d v g (u)≤ n log(A opt‖ D u‖ BV (M)+ B opt) for all u∈ BV (M) with‖ u‖ L 1 (M)= 1 and existence of extremal functions. In particular, we prove that this optimal inequality is equivalent to an optimal L 1-Sobolev inequality obtained by Druet [3].
Elsevier