Symmetry properties in higher order semilinear elliptic equations

1995 ◽  
Vol 24 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Robert Dalmasso
Keyword(s):  
Elliptic Equations ◽  
Higher Order ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Symmetry Properties

scholarly journals MAXIMUM PRINCIPLES FOR SOME HIGHER-ORDER SEMILINEAR ELLIPTIC EQUATIONS

2010 ◽  
Vol 53 (2) ◽  
pp. 313-320 ◽  
Author(s):  
A. MARENO
Keyword(s):  
Elliptic Equations ◽  
Auxiliary Function ◽  
Higher Order ◽  
Semilinear Elliptic Equations ◽  
Maximum Principles ◽  
Eighth Order ◽  
Analyse Math ◽  
Semilinear Elliptic

AbstractWe deduce maximum principles for fourth-, sixth- and eighth-order elliptic equations by modifying an auxiliary function introduced by Payne (J. Analyse Math. 30 (1976), 421–433). Integral bounds on various gradients of the solutions of these equations are obtained.

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 A Note on the Complete Rotational Invariance of Biradial Solutions to Semilinear Elliptic Equations

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
L. Abatangelo ◽  
S. Terracini
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Rotational Invariance ◽  
Solutions To Equations ◽  
Semilinear Elliptic ◽  
Symmetry Properties

AbstractWe investigate symmetry properties of solutions to equations of the form-Δu =in ℝ

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