Hadamard-type formulas via the Maslov form

@article{Latushkin2016HadamardtypeFV,
  title={Hadamard-type formulas via the Maslov form},
  author={Yuri Latushkin and Alim Sukhtayev},
  journal={Journal of Evolution Equations},
  year={2016},
  volume={17},
  pages={443-472}
}
Given a star-shaped bounded Lipschitz domain $${\Omega\subset{\mathbb{R}}^d}$$Ω⊂Rd, we consider the Schrödinger operator $${L_{\mathcal{G}}=-\Delta+V}$$LG=-Δ+V on $${\Omega}$$Ω and its restrictions $${L^{\Omega_t}_{\mathcal{G}}}$$LGΩt on the subdomains $${\Omega_t}$$Ωt, $${t\in[0,1]}$$t∈[0,1], obtained by shrinking $${\Omega}$$Ω toward its center. We impose either the Dirichlet or quite general Robin-type boundary conditions determined by a subspace $${{\mathcal{G}}}$$G of the boundary space… 
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