Kristaly, A. (2019) Journal of Functional Analysis [Matematică, Q1]

Publicat: 05 Noiembrie 2020

Kristaly, A. (2019) New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case. Journal of Functional Analysis, 276(8), 2359-2396

DOI: https://doi.org/10.1016/j.jfa.2019.01.008

✓ Publisher: Elsevier
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics
✓ Article Influence Score (AIS): 1.653 (2019) / Q1

Abstract: In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform estimates via Gromov's covering lemma, we provide a Coulhon, Saloff-Coste and Varopoulos type characterization concerning the validity of Moser-Trudinger inequalities on complete non-compact n-dimensional Riemannian manifolds (n >= 2) with Ricci curvature bounded from below. Some sharp consequences are also presented both for non-negatively and non-positively curved Riemannian manifolds, respectively. In the second part, by combining variational arguments and a Lions type symmetrization-compactness principle, we guarantee the existence of a non-zero isometry-invariant solution for an elliptic problem involving the n-Laplace-Beltrami operator and a critical nonlinearity on n-dimensional homogeneous Hadamard manifolds. Our results complement in several directions those of Y. Yang.

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