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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 …
manifold $\mathbb {M}^ n $, the isoperimetric inequality holds with Euclidean optimal …
Lp gradient estimates and Calderón–Zygmund inequalities under Ricci lower bounds
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 …
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
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 …
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 …
problems on Riemannian manifold. In Part I, we focus on solutions to the Poisson equation …
Gradient estimates under integral Ricci bounds
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 …
on Riemannian manifolds. Under integral (lower) bounds on the Ricci tensor we prove the …