scholarly journals Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations

2014 ◽  
Vol 61 (2) ◽  
pp. 373-408 ◽  
Author(s):  
K. Krumbiegel ◽  
J. Pfefferer
Keyword(s):  
Boundary Control ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Semilinear Elliptic Equations ◽  
Control Problems ◽  
Semilinear Elliptic ◽  
Boundary Control Problems

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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