scholarly journals Uniform anti-maximum principle for polyharmonic boundary value problems

2000 ◽  
Vol 129 (2) ◽  
pp. 467-474 ◽  
Author(s):  
Philippe Clément ◽  
Guido Sweers
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Boundary Value

SYMMETRY RESULT FOR SOME OVERDETERMINED VALUE PROBLEMS

2008 ◽  
Vol 49 (4) ◽  
pp. 479-494 ◽  
Author(s):  
MOHAMMED BARKATOU ◽  
SAMIRA KHATMI
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Neumann Problem ◽  
Compatibility Condition ◽  
Mean Curvature ◽  
Boundary Value ◽  
The Maximum Principle ◽  
The Mean ◽  
The Neumann Problem ◽  
Symmetry Result

AbstractThe aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

Energy and pointwise bounds in some non-standard parabolic problems

2004 ◽  
Vol 134 (1) ◽  
pp. 1-9 ◽  
Author(s):  
K. A. Ames ◽  
L. E. Payne ◽  
P. W. Schaefer
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Parabolic Problems ◽  
Differential Inequalities ◽  
Initial Boundary Value Problems ◽  
Auxiliary Condition ◽  
Image Position ◽  
Initial Boundary Value

We study a class of initial-boundary-value problems for which an auxiliary condition of the form is prescribed. We determine bounds on an energy expression by means of differential inequalities and derive pointwise bounds for the solution and its gradient by use of a parabolic maximum principle.

SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION

2001 ◽  
Vol 11 (06) ◽  
pp. 1073-1080 ◽  
Author(s):  
G. A. PHILIPPIN ◽  
A. SAFOUI
Keyword(s):  
Maximum Principle ◽  
Boundary Conditions ◽  
Recent Result ◽  
Boundary Value Problems ◽  
Differential Inequality ◽  
Boundary Value ◽  
Maximum Principles ◽  
Maximum Value ◽  
Symmetry Properties ◽  
Monge Ampere

In this paper we investigate a class of boundary value problems for the Monge-Ampère equation [Formula: see text] where Ω is a strictly convex bounded domain in RN, N≥2. When f=g(u)h(|∇u|2) with g and h satisfying the differential inequality [Formula: see text] we show in Sec. 2 that the function [Formula: see text] takes its maximum value on the boundary ∂Ω. This maximum principle generalizes a recent result of Ma who investigated the case f= const in R2. In Sec. 3 we investigate symmetry properties of u under specific boundary conditions or geometry of Ω.

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