scholarly journals A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class

2017 ◽  
Vol 10 (4) ◽  
pp. 853-866 ◽  
Author(s):  
Fabio Paronetto ◽  
Keyword(s):  
Maximum Principle ◽  
Type Inequality ◽  
Harnack Type Inequality

scholarly journals Maximum principle for higher order operators in general domains

2021 ◽  
Vol 11 (1) ◽  
pp. 655-671
Author(s):  
Daniele Cassani ◽  
Antonio Tarsia
Keyword(s):  
Maximum Principle ◽  
Type Inequality ◽  
Higher Order ◽  
Elliptic Operators ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Even Order ◽  
Harnack Type Inequality

Abstract We first prove De Giorgi type level estimates for functions in W 1,t (Ω), Ω ⊂ R N $ \Omega\subset{\mathbb R}^N $ , with t > N ≥ 2 $ t \gt N\geq 2 $ . This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtained in Di Benedetto–Trudinger [10] for functions in W 1,2(Ω). As a consequence, we prove the validity of the strong maximum principle for uniformly elliptic operators of any even order, in fairly general domains in dimension two and three, provided second order derivatives are taken into account.

scholarly journals A fully nonlinear version of the Yamabe problem and a Harnack type inequality

2003 ◽  
Vol 336 (4) ◽  
pp. 319-324 ◽  
Author(s):  
Aobing Li ◽  
Yan Yan Li
Keyword(s):  
Type Inequality ◽  
Yamabe Problem ◽  
Fully Nonlinear ◽  
Nonlinear Version ◽  
Harnack Type Inequality

scholarly journals Harnack Type Inequality: the Method of Moving Planes

1999 ◽  
Vol 200 (2) ◽  
pp. 421-444 ◽  
Author(s):  
Yan Yan Li
Keyword(s):  
Type Inequality ◽  
Method Of Moving Planes ◽  
Moving Planes ◽  
Harnack Type Inequality

COMPLETE WEINGARTEN HYPERSURFACES SATISFYING AN OKUMURA TYPE INEQUALITY

2019 ◽  
Vol 109 (1) ◽  
pp. 81-92 ◽  
Author(s):  
EUDES L. DE LIMA ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Riemannian Space ◽  
Type Inequality ◽  
Type Operator ◽  
Space Forms ◽  
Totally Umbilical ◽  
Linear Weingarten Hypersurfaces ◽  
Riemannian Space Forms

In this paper we deal with complete linear Weingarten hypersurfaces immersed into Riemannian space forms. Assuming an Okumura type inequality on the total umbilicity tensor of such hypersurfaces, we prove that either the hypersurface is totally umbilical or it holds an estimate for the norm of the total umbilicity tensor, which is also shown be sharp in the sense that the product of space forms realize them. Our approach is based on a version of the Omori–Yau maximum principle for a suitable Cheng–Yau type operator.

A Harnack-Type Inequality for a Prescribed-Curvature Equation on a Domain with Boundary

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Mathew R. Gluck ◽  
Ying Guo ◽  
Lei Zhang
Keyword(s):  
Positive Solutions ◽  
Type Inequality ◽  
Curvature Equation ◽  
Prescribed Curvature ◽  
Harnack Type Inequality ◽  
Moving Spheres

AbstractIn this paper the method of moving spheres is used to derive a Harnack-type inequality for positive solutions ofwhere n ≥ 4, ℝ.

A Harnack type inequality for the Yamabe equation in low dimensions

2004 ◽  
Vol 20 (2) ◽  
pp. 133-151 ◽  
Author(s):  
Lei Zhang ◽  
YanYan Li
Keyword(s):  
Type Inequality ◽  
Low Dimensions ◽  
Yamabe Equation ◽  
Harnack Type Inequality

Geometric character of domain and the Harnack inequality of solution of a singular parabolic equation

2012 ◽  
Vol 62 (4) ◽  
Author(s):  
Jiaqing Pan
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Neumann Boundary Condition ◽  
Type Inequality ◽  
Neumann Boundary ◽  
Space Time ◽  
Singular Parabolic Equation ◽  
Geometric Character ◽  
Harnack Type Inequality

AbstractThe geometric character of domains of solutions of a singular parabolic equation with the Neumann boundary condition are discussed in this work. We prove a gradient estimate and a Harnack type inequality and then, show that the domains of the solutions are exactly columns in the space-time. Specially, the altitudes of the columns are calculated accurately.

Harnack‐type inequality for fractional elliptic equations with critical exponent

2020 ◽  
Vol 43 (8) ◽  
pp. 5380-5397 ◽  
Author(s):  
Shuibo Huang ◽  
Qiaoyu Tian
Keyword(s):  
Critical Exponent ◽  
Elliptic Equations ◽  
Type Inequality ◽  
Harnack Type Inequality

scholarly journals A Harnack type inequality for certain complex Monge-Ampère equations

1989 ◽  
Vol 29 (3) ◽  
pp. 481-488 ◽  
Author(s):  
Gang Tian
Keyword(s):  
Type Inequality ◽  
Harnack Type Inequality ◽  
Monge Ampere

scholarly journals Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces

2019 ◽  
Vol 31 (4) ◽  
pp. 1007-1026 ◽  
Author(s):  
Ewa Damek ◽  
Zeineb Ghardallou
Keyword(s):  
Sufficient Conditions ◽  
Type Inequality ◽  
Beltrami Operator ◽  
Continuous Solutions ◽  
Large Solutions ◽  
Rank One ◽  
Harnack Type Inequality ◽  
Necessary And Sufficient ◽  
The Laplace Operator ◽  
Noncompact Symmetric Space

Abstract Let {\mathcal{L}} be the Laplace operator on {\mathbb{R}^{d}} , {d\geq 3} , or the Laplace–Beltrami operator on the harmonic NA group (in particular, on a rank one noncompact symmetric space). For the equation {\mathcal{L}u-\varphi(\,\cdot\,,u)=0} we give necessary and sufficient conditions for the existence of entire bounded or large solutions under the hypothesis of radiality of φ with respect to the first variable. A Harnack-type inequality for positive continuous solutions is also proved.

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