scholarly journals On the Stability of Solutions of Semilinear Elliptic Equations with Robin Boundary Conditions on Riemannian Manifolds

2016 ◽  
Vol 48 (1) ◽  
pp. 122-151 ◽  
Author(s):  
C. Bandle ◽  
P. Mastrolia ◽  
D. D. Monticelli ◽  
F. Punzo
Keyword(s):  
Boundary Conditions ◽  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Robin Boundary Conditions ◽  
Stability Of Solutions ◽  
Semilinear Elliptic ◽  
The Stability ◽  
Robin Boundary

scholarly journals Maximum principles for a class of semilinear elliptic boundary-value problems

1995 ◽  
Vol 52 (1) ◽  
pp. 169-175 ◽  
Author(s):  
Zhang Hailiang
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Elliptic Boundary ◽  
Maximum Principles ◽  
Robin Boundary Conditions ◽  
Elliptic Boundary Value ◽  
Physical Problems ◽  
Semilinear Elliptic ◽  
Robin Boundary

For years it has remained a problem to find suitable functionals satisfying certain maximum principles for solutions of the equation Δu + f(x, u) = 0. In this paper, maximum principles for certain functionals which are defined on solutions of semilinear elliptic equations subject to mixed or Robin boundary conditions are obtained. The principles derived may be used to deduce bounds on important quantities in physical problems of interest.

Symmetry properties of positive solutions of elliptic equations in an infinite sectorial cone

1992 ◽  
Vol 122 (1-2) ◽  
pp. 137-160
Author(s):  
Chie-Ping Chu ◽  
Hwai-Chiuan Wang
Keyword(s):  
Boundary Conditions ◽  
Positive Solution ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Semilinear Elliptic Equations ◽  
Spherically Symmetric ◽  
Semilinear Elliptic ◽  
Symmetry Properties

SynopsisWe prove symmetry properties of positive solutions of semilinear elliptic equations Δu + f(u) = 0 with Neumann boundary conditions in an infinite sectorial cone. We establish that any positive solution u of such equations in an infinite sectorial cone ∑α in ℝ3 is spherically symmetric if the amplitude α of ∑α is not greater than π.

scholarly journals Existence and Stability of Solutions of General Semilinear Elliptic Equations with Measure Data

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Laurent Véron
Keyword(s):  
Elliptic Equations ◽  
Measure Data ◽  
Unified Theory ◽  
Stability Of Solutions ◽  
Semilinear Elliptic ◽  
The Poisson Equation ◽  
Order Elliptic Operator ◽  
Carathéodory Function ◽  
Existence And Stability ◽  
The Stability

AbstractWe study existence and stability for solutions of −Lu + g(x, u) = ω where L is a second order elliptic operator, g a Caratheodory function and ω a measure in Ω. We present a unified theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.

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