Zobrazeno 1 - 10
of 3 568
pro vyhledávání: '"Liouville theorems"'
In this paper, we prove two Liouville theorems for harmonic metrics on complex flat line bundles on gradient steady Ricci solitons and gradient shrinking K\"{a}hler-Ricci solitons, which imply that they arise from fundamental group representations in
Externí odkaz:
http://arxiv.org/abs/2411.12012
We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of positive solutions to the subcritical Lane-Emden-Fowler equations over
Externí odkaz:
http://arxiv.org/abs/2411.06956
In this paper we study positive solutions to the CR Yamabe equation in noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. In particular, we show that the Heisenberg group $\mathbb{H}^1$ is the only (complete) Sasakian spac
Externí odkaz:
http://arxiv.org/abs/2412.08500
Autor:
Chen, Qun, Qiu, Hongbing
When the domain is a complete noncompact Riemannian manifold with nonnegative Bakry--Emery Ricci curvature and the target is a complete Riemannian manifold with sectional curvature bounded above by a positive constant, by carrying out refined gradien
Externí odkaz:
http://arxiv.org/abs/2412.04684
Autor:
Chipot, Michel, Hauer, Daniel
The goal of this note is to consider Liouville type theorem for p-Laplacian type operators. In particular guided by the Laplacian case one establishes analogous results for the p-Laplacian and operators of this type.
Comment: Key words: p-Laplac
Comment: Key words: p-Laplac
Externí odkaz:
http://arxiv.org/abs/2411.09274
Autor:
Quittner, Pavol, Souplet, Philippe
We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based on the corresponding elliptic Liouville type theorems and energy estim
Externí odkaz:
http://arxiv.org/abs/2409.20049
Autor:
Priola Enrico
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 12, Iss 1, Pp 221-254 (2024)
It is known that for a possibly degenerate hypoelliptic Ornstein-Uhlenbeck (OU) operator L=12tr(QD2)+⟨Ax,D⟩=12div(QD)+⟨Ax,D⟩,x∈RN,L=\frac{1}{2}\hspace{0.1em}\text{tr}\hspace{0.1em}\left(Q{D}^{2})+\langle Ax,D\rangle =\frac{1}{2}\hspace{0.1e
Externí odkaz:
https://doaj.org/article/14292faec25245f09563977f7d404a17
In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique, to establish Liouville property of the solutions. We also answer an op
Externí odkaz:
http://arxiv.org/abs/2407.16147
Autor:
Quittner, Pavol, Souplet, Philippe
We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and Schr\"odinger type systems. This applies to various classes of nonlineariti
Externí odkaz:
http://arxiv.org/abs/2407.04154
Autor:
Priola, Enrico
It is known that for a possibly degenerate hypoelliptic Ornstein-Uhlenbeck operator $$ L= \frac{1}{2}\text{ tr} (QD^2 ) + \langle Ax, D \rangle = \frac{1}{2}\text{ div} (Q D ) + \langle Ax, D \rangle,\;\; x \in R^N, $$ all (globally) bounded solution
Externí odkaz:
http://arxiv.org/abs/2405.03410