On Solvability of Second-Order Semilinear Elliptic Equations on Spheres

2021 ◽  
Author(s):  
Dmitry V. Tunitsky
Keyword(s):  
Elliptic Equations ◽  
Second Order ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic

A remark on comparison results via symmetrization

1986 ◽  
Vol 102 (1-2) ◽  
pp. 37-48 ◽  
Author(s):  
A. Alvino ◽  
P.L. Lions ◽  
G. Trombetti
Keyword(s):  
Elliptic Equations ◽  
Second Order ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Comparison Results ◽  
Second Order Elliptic Equations

SynopsisIn this paper, we study the converse of comparison results for solutions to linear second-order elliptic equations. Namely, in the inequalities proved by G. Talenti and others, we study the case of equality and prove that “equalities are achieved only in the spherical situation”. We also present some applications of these results to semilinear elliptic equations.

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