p-Energia in spazi metrici generalizzati

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 . 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 σ_r 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