Réunion d'hiver SMC 2026
Montréal, 11 - 14 décembre 2026
EDP non-linéaires et géométriques
Org: Joshua Flynn (Massachusetts Institute of Technology) et Jérôme Vétois (McGill University)
[PDF]
Org: Joshua Flynn (Massachusetts Institute of Technology) et Jérôme Vétois (McGill University)
[PDF]
- LORENZO CARLETTI, University of Oxford
- NGUYEN LAM, Memorial University of Newfoundland
Doubly sharp Poincaré–Sobolev inequalities on hyperbolic spaces [PDF]
- NGUYEN LAM, Memorial University of Newfoundland
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We study when one can subtract the full spectral gap $\left(\frac{N-1}{p}\right)^p$ of the $p$-Laplacian on the hyperbolic space $\mathbb{H}^N$ and still keep the sharp Euclidean Sobolev constant. Using a change of function which keeps the $L^p$ norm, together with a one-dimensional tangent line inequality, we establish such doubly sharp inequalities with explicit remainder terms in new ranges of $p$, including $N=3$ and $2\leq p<3$. The same method also gives sharp logarithmic Sobolev inequalities with the full spectral gap. This is joint work with A. X. Do, D. Ganguly and G. Lu.
- GALEN NOVELLO, University of New Mexico
- RAQUEL PERALES, Centro de Investigación en Mátematicas, Guanaujato
- JACOB REZNIKOV, Massachussets Institute of Technology
- DIMITER VASSILEV, University of New Mexico
Regularity of Solutions to Non-Local Operators on Homogeneous Groups [PDF]
- RAQUEL PERALES, Centro de Investigación en Mátematicas, Guanaujato
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We prove a Harnack inequality and show H\"older continuity of solutions to non-linear nonlocal operators on homogeneous groups.
- SAMUEL ZEITLER, Carnegie Mellon University