SomeL 1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions

1988 ◽  
Vol 17 (1) ◽  
pp. 203-224 ◽  
Author(s):  
Philippe Benilan ◽  
Michael G. Crandall ◽  
Paul Sacks
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic

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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