Symmetry for elliptic equations in a half-space without strong maximum principle

2004 ◽  
Vol 134 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Yihong Du ◽  
Zongming Guo
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Precise Determination ◽  
Strong Maximum Principle ◽  
New Approach ◽  
Lipschitz Continuous ◽  
Weak Maximum Principle ◽  
Image Position ◽  
Symmetry Result

For a wide class of nonlinearities f(u) satisfying but not necessarily Lipschitz continuous, we study the quasi-linear equation where T = {x = (x1, x2, …, xN) ∈ RN: x1 > 0} with N ≥ 2. By using a new approach based on the weak maximum principle, we show that any positive solution on T must be a function of x1 only. Under our assumptions, the strong maximum principle does not hold in general and the solution may develop a flat core; our symmetry result allows an easy and precise determination of the flat core.

DISCRETE CONSERVATION AND DISCRETE MAXIMUM PRINCIPLE FOR ELLIPTIC PDEs

1998 ◽  
Vol 08 (04) ◽  
pp. 685-711 ◽  
Author(s):  
ENRICO BERTOLAZZI
Keyword(s):  
Maximum Principle ◽  
Differential Operator ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Numerical Solutions ◽  
Strong Maximum Principle ◽  
Discrete Maximum Principle ◽  
Elliptic Pdes ◽  
Numerical Schemes

A class of finite volume numerical schemes for the solution of self-adjoint elliptic equations is described. The main feature of the schemes is that numerical solutions share both discrete conservation and discrete strong maximum principle without restriction on the differential operator or on the volume elements.

scholarly journals On the strong maximum principle for parabolic differential equations

1986 ◽  
Vol 29 (1) ◽  
pp. 93-96 ◽  
Author(s):  
Wolfgang Walter
Keyword(s):  
Maximum Principle ◽  
Differential Equations ◽  
Heat Equation ◽  
Nonlinear Equations ◽  
Strong Maximum Principle ◽  
Parabolic Differential Equations ◽  
Carry Over ◽  
Image Position

In a recent paper [2], D. Colton has given a new proof for the strong maximum principle with regard to the heat equation ut = Δu. His proof depends on the analyticity (in x) of solutions. For this reason it does not carry over to the equationor to more general equations. But in order to tread mildly nonlinear equations such asut = Δu + f(u) which are important in many applications, it is essential to have the strong maximum principle at least for equation (*). It should also be said that this proof uses nontrivial facts about the heat equation.

New approach to precise determination of the capacity of an adsorption monolayer

2006 ◽  
Vol 68 (5) ◽  
pp. 654-654
Author(s):  
G. I. Berezin ◽  
K. O. Murdmaa ◽  
A. A. Fomkin
Keyword(s):  
Precise Determination ◽  
New Approach ◽  
Adsorption Monolayer

scholarly journals Maximum principle for non-linear degenerate equations of the parabolic type

1982 ◽  
Vol 25 (2) ◽  
pp. 251-263 ◽  
Author(s):  
Jan Chabrowski ◽  
Rudolf Výborný
Keyword(s):  
Maximum Principle ◽  
Differential Inequality ◽  
Parabolic Type ◽  
Degenerate Equations ◽  
Weak Maximum Principle ◽  
Degenerate Parabolic ◽  
The Difference ◽  
Image Position ◽  
Linear Degenerate ◽  
Nonlinear Degenerate

This paper establishes a weak maximum principle for the difference u − v of solutions to nonlinear degenerate parabolic differential inequality

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

2020 ◽  
Vol 20 (2) ◽  
pp. 503-510
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Strong Maximum Principle ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Natural Growth ◽  
Dirichlet Problems ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractIn this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.

A New Approach to IDDQ Failure Fault Localization Using Single Shot Logic (SSL) Patterns

2019 ◽  
Author(s):  
Rommel Estores ◽  
Stefaan Verleye
Keyword(s):  
Fault Location ◽  
Fault Localization ◽  
Internal Node ◽  
Precise Determination ◽  
Control Individual ◽  
Single Shot ◽  
New Approach ◽  
Measurement Results ◽  
Defective Area

Abstract In this paper the authors will discuss an application of Single Shot Logic (SSL) patterns used for further localizing IDDQ failures using ATPG constraints and targeted faults. This new method provides the analyst a possibility of performing circuit analysis using IDDQ measurement results as a pass/fail criterion rather than logic mismatches. Once a defective area was partially isolated through fault localization, SSL patterns were created to control individual internal node logic states in a deterministic way. IDDQ was measured at each SSL iteration where schematic analysis can further isolate the failure to a specific location. Two case studies will be discussed to show how this technique was used on actual failing units, with detailed explanation of the steps performed that led to a more precise determination of the fault location in the suspect cell.

General uniqueness results and blow-up rates for large solutions of elliptic equations

2012 ◽  
Vol 142 (4) ◽  
pp. 825-837 ◽  
Author(s):  
Shuibo Huang ◽  
Wan-Tong Li ◽  
Qiaoyu Tian ◽  
Yongsheng Mi
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
Variation Theory ◽  
Singular Boundary ◽  
Smooth Bounded Domain ◽  
Lipschitz Continuous ◽  
Large Solutions ◽  
Uniqueness Results ◽  
Locally Lipschitz ◽  
Image Position

Making use of the Karamata regular variation theory and the López-Gómez localization method, we establish the uniqueness and asymptotic behaviour near the boundary ∂Ω for the large solutions of the singular boundary-value problemwhere Ω is a smooth bounded domain in ℝN. The weight function b(x) is a non-negative continuous function in the domain, which can vanish on the boundary ∂Ω at different rates according to the point x0 ∊ ∂Ω. f(u) is locally Lipschitz continuous such that f(u)/u is increasing on (0, ∞) and f(u)/up = H(u) for sufficiently large u and p > 1, here H(u) is slowly varying at infinity. Our main result provides a sharp extension of a recent result of Xie with f satisfying limu→f(u)/up = H for some positive constants H > 0 and p > 1.

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