scholarly journals On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions

2017 ◽  
Vol 7 (3) ◽  
pp. 493-506
Author(s):  
Shu Luan ◽  
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Existence Of Optimal Control ◽  
Nonlinear Neumann Boundary Conditions

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.

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