A remark on minimization of an energy type functional
Abstract
We study the problem of the minimization of the energy type functional
Φ(f)=∫Ωf G f
on a class of function with prescribed distribution function that we denote by C(f0). We will prove that there exists only one minimizer of the functional considered in the weak closure of C(f0). We find some conditions that f0 has to verify in order to have the minimizer in C(f0).
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