Differentiation of the functional in a parametric optimization problem for a coefficient of a semilinear elliptic equation

2017 ◽  
Vol 53 (4) ◽  
pp. 551-562 ◽  
Author(s):  
A. V. Chernov
Keyword(s):  
Elliptic Equation ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic ◽  
Parametric Optimization Problem

scholarly journals Necessary conditions for optimal control of elliptic systems

2000 ◽  
Vol 41 (4) ◽  
pp. 542-567 ◽  
Author(s):  
Hang Gao ◽  
Xunjing Li
Keyword(s):  
Optimal Control ◽  
Elliptic Equation ◽  
Optimization Problem ◽  
Necessary Conditions ◽  
Elliptic Systems ◽  
Semilinear Elliptic Equation ◽  
Optimal Domain ◽  
Domain Optimization ◽  
Semilinear Elliptic

AbstractIn this paper, we consider the system governed via the coefficients of a semilinear elliptic equation and give the necessary conditions for optimal control. Furthermore, we obtain the necessary conditions for an optimal domain in a domain optimization problem.

Positive Solutions for Elliptic Equations With Supercritical Nonlinearity

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
Paulo Rabelo
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Auxiliary Problem ◽  
Semilinear Elliptic Equation ◽  
Minimax Methods ◽  
Semilinear Elliptic ◽  
Priori Estimates ◽  
Supercritical Nonlinearity

AbstractIn this paper minimax methods are employed to establish the existence of a bounded positive solution for semilinear elliptic equation of the form−∆u + V (x)u = P(x)|u|where the nonlinearity has supercritical growth and the potential can change sign. The solutions of the problem above are obtained by proving a priori estimates for solutions of a suitable auxiliary problem.

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