Results 21 to 30 of about 239 (57)

Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation [PDF]

, 2018
Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align ...
Abimbola Abolarinwa, Bakry, Brandolini, Brighton, Bǎileşteanu, Cao, Case, Case, Chen, Cheng, Del Pino, Hamilton, Hamilton, Ledoux, Li, Li, Ma, Mastrolia, Ruan, Souplet, Wang, Wei, Wu, Wu, Wu, Wu, Yang, Yau, Zhu, Zhu, Zhu   +30 more
core   +2 more sources

Higher-dimensional solutions for a nonuniformly elliptic equation

, 2013
We prove $m$-dimensional symmetry results, that we call $m$-Liouville theorems, for stable and monotone solutions of the following nonuniformly elliptic equation \begin{eqnarray*}\label{mainequ} - div(\gamma(\mathbf x') \nabla u(\mathbf x)) =\lambda ...
Fazly, Mostafa
core   +1 more source

Liouville theorems for a family of very degenerate elliptic non linear operators

, 2017
We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators ${\cal P}^\pm_k$, defined respectively as the sum of the largest and the smallest $k ...
Birindelli, Isabeau, Galise, Giulio, Leoni, Fabiana   +2 more
core   +1 more source

Radial symmetry, monotonicity and Liouville theorem for Marchaud fractional parabolic equations with the nonlocal Bellman operator

Advanced Nonlinear Studies
In this article, we focus on studying space-time fractional parabolic equations with the nonlocal Bellman operator and the Marchaud fractional derivative. To address the difficulty caused by the space-time non-locality of operator ∂tα−Fs ${\partial }_{t}^
Liu Mengru, Zhang Lihong, Wang Guotao
doaj   +1 more source

Quasilinear elliptic equations with critical potentials

Advances in Nonlinear Analysis, 2017
We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj   +1 more source

Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
doaj   +1 more source

A Liouville theorem for the Degasperis-Procesi equation [PDF]

, 2015
We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution.
Brandolese, Lorenzo
core  

A view on Liouville theorems in PDEs

Analysis and Geometry in Metric Spaces
Our review of Liouville theorems includes a special focus on nonlinear partial differential equations and inequalities.
Mitidieri Enzo
doaj   +1 more source

A Refined Approach for Non-Negative Entire Solutions of Δ u + up = 0 with Subcritical Sobolev Growth

Advanced Nonlinear Studies, 2017
Let N≥2{N\geq 2} and ...
Villavert John
doaj   +1 more source

Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities [PDF]

, 2010
We study fully nonlinear elliptic equations such as \[ F(D^2u) = u^p, \quad p>1, \] in $\R^n$ or in exterior domains, where $F$ is any uniformly elliptic, positively homogeneous operator.
Armstrong, Scott N., Sirakov, Boyan
core   +4 more sources