Abstract
Given a setS and a function σ:S x S→[0, +∞[ such that σ(x, x)=0, we define the generalizedp-energy of a curve γ: [a, b]→S, so that, ifS is a Hilbert space and σ(x, y)=‖x−y‖ we obtain\(\smallint _a^b \left\| {\dot \Upsilon } \right\|^p dt\). Sufficient conditions for the equality of the defined energies are also given. Moreover the case in whichS is a set of measurable parts of ℝn and σr is a family of functions used in order to study the generalized minimizing motions, is discussed.
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Conferenza tenuta il 30 ottobre 1995
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Palmieri, G. p-Energia in spazi metrici generalizzati. Seminario Mat. e. Fis. di Milano 65, 335–356 (1995). https://doi.org/10.1007/BF02925264
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DOI: https://doi.org/10.1007/BF02925264