Geodesic
Variational formulae for conformal capacity
Sbornik. Mathematics, Tome 215 (2024) no. 1, pp. 90-100

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Analogues of Hadamard's classical variational formula are presented for the Dirichlet integral of a normalized harmonic function under deformations of its domain of definition. Variational formulae for quadratic forms with coefficients depending on the inner radii, Robin radii, Green's functions and Robin functions of the domains under consideration are also presented. Bibliography: 17 titles.
Keywords: conformal capacity, Dirichlet integral, Robin function, Robin capacity.
Mots-clés : variational formulae 
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V. N. Dubinin. Variational formulae for conformal capacity. Sbornik. Mathematics, Tome 215 (2024) no. 1, pp. 90-100. http://geodesic.mathdoc.fr/item/SM_2024_215_1_a4/