We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving plane method to find symmetry results for solutions of a system. We apply these results to discuss symmetry for the maximal configurations of the previous problem.
Symmetry of solutions to optimization problems related to partial differential equations
CUCCU, FABRIZIO;
2006-01-01
Abstract
We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving plane method to find symmetry results for solutions of a system. We apply these results to discuss symmetry for the maximal configurations of the previous problem.
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