Abstract
Given a bounded open set Ω of Rn, n ≥ 2, and α $\in$ R, let us consider $$\mu(\Omega,\alpha)=\min_{\substack{v\in W_{0}^{1,2}(\Omega)\\v\not\equiv 0}} \frac{{\Large\int}_{\Omega} |\nabla v|^{2}dx+\alpha \left|{\Large\int}_{\Omega}|v|v\,dx \right|}{{\Large\int}_{\Omega} |v|^{2}dx}.$$ We study some properties of μ(Ω,α) and of its minimizers, and, depending on α, we determine the sets Ωα among those of fixed measure such that μ(Ωα,α) is the smallest possible.
Citation
Francesco Della Pietra. "Some remarks on a shape optimization problem." Kodai Math. J. 37 (3) 608 - 619, October 2014. https://doi.org/10.2996/kmj/1414674612
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