scholarly journals Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations

2000 ◽  
Vol 38 (5) ◽  
pp. 1369-1391 ◽  
Author(s):  
Eduardo Casas ◽  
Fredi Tröltzsch ◽  
Andreas Unger
Keyword(s):  
Optimality Conditions ◽  
Elliptic Equations ◽  
Second Order ◽  
Semilinear Elliptic Equations ◽  
Control Problems ◽  
Sufficient Optimality Conditions ◽  
Constrained Control ◽  
Semilinear Elliptic ◽  
Constrained Control Problems

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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