Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds

M Muratori, N Soave - arxiv preprint arxiv:2103.08240, 2021 - arxiv.org
The Cartan-Hadamard conjecture states that, on every $ n $-dimensional Cartan-Hadamard
manifold $\mathbb {M}^ n $, the isoperimetric inequality holds with Euclidean optimal …

Lp gradient estimates and Calderón–Zygmund inequalities under Ricci lower bounds

L Marini, S Meda, S Pigola… - Revista matemática …, 2024 - content.ems.press
In this paper, we investigate the validity of first and second order Lp estimates for the
solutions of the Poisson equation depending on the geometry of the underlying manifold …

On the Liouville property for fully nonlinear equations with superlinear first-order terms

M Cirant, A Goffi - … of the conference “Geometric and Functional …, 2023 - books.google.com
We consider in this note one-side Liouville properties for viscosity solutions of various fully
nonlinear uniformly elliptic inequalities, whose prototype is F (x, D2u)≥ Hi (x, u, Du) in RN …

Global estimates and positivity preservation for some elliptic PDEs on Riemannian manifolds.

L Marini - 2023 - boa.unimib.it
This dissertation deals with certain qualitative properties for the solutions of two elliptic
problems on Riemannian manifold. In Part I, we focus on solutions to the Poisson equation …

Gradient estimates under integral Ricci bounds

L Marini, S Pigola, G Veronelli - arxiv preprint arxiv:2204.04002, 2022 - arxiv.org
In this paper we study $ W^{1, p} $ global regularity estimates for solutions of $\Delta u= f $
on Riemannian manifolds. Under integral (lower) bounds on the Ricci tensor we prove the …