Advances in Nonlinear Analysis, 2014 We obtain a new Liouville comparison principle for weak solutions (u,v) of semilinear parabolic second-order partial differential inequalities of the form ut-ℒu-|u|q-1u≥vt-ℒv-|v|q-1v(*)$u_t -{\mathcal {L}}u- |u|^{q-1}u\ge v_t -{\mathcal {L}}v- |v|^{q-1}v\
Kurta Vasilii V.
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Liouville properties and critical value of fully nonlinear elliptic operators [PDF]
, 2016 We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate
Bardi, Martino, Cesaroni, Annalisa
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Some properties of solutions to weakly hypoelliptic equations [PDF]
, 2013 A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size.
Baer, Christian
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A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient
Advanced Nonlinear Studies, 2020 We consider the elliptic equation -Δu=uq|∇u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.
Filippucci Roberta +2 more
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Phragmén-Lindelöf alternative for the Laplace equation with dynamic boundary conditions [PDF]
, 2017 This paper investigates the spatial behavior of the solutions of the Laplace equation on a semi-infinite cylinder when dynamical nonlinear boundary conditions are imposed on its lateral side.
Leseduarte Milán, María Carme +1 more
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Positive Solutions for Systems of Quasilinear Equations with Non-homogeneous Operators and Weights
Advanced Nonlinear Studies, 2020 In this paper we deal with positive radially symmetric solutions for a boundary value problem containing a strongly nonlinear operator. The proof of existence of positive solutions that we give uses the blow-up method as a main ingredient for the search ...
García-Huidobro Marta +2 more
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On the uniqueness of $L_p$-Minkowski problems: the constant $p$-curvature case in $\mathbb{R}^3$ [PDF]
, 2015 We study the $C^4$ smooth convex bodies $\mathbb{K}\subset\mathbb{R}^{n+1}$ satisfying $K(x)=u(x)^{1-p}$, where $x\in\mathbb{S}^n$, $K$ is the Gauss curvature of $\partial\mathbb{K}$, $u$ is the support function of $\mathbb{K}$, and $p$ is a constant. In
Andrews +49 more
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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 +30 more
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Remarks on two fourth order elliptic problems in whole space
, 2014 We are interested in entire solutions for the semilinear biharmonic equation $\Delta^{2}u=f(u)$ in $\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-\Delta u>0$ without any ...
Lai, Baishun, Ye, Dong
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Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential [PDF]
, 2010 We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u):= - pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and ...
Fraas, Martin, Pinchover, Yehuda
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