For a bounded domain Ω ⊂ Rn let HΩ : Ω ×Ω → R be the regular part of the Dirichlet Green function for the Laplace operator. Given a fixed arbitrary C2 function f : D → R, defined on an open subset D ⊂ RnN, and fixed coefficients λ1, . . ., λN ∈ R{0} we consider the function fΩ: D∩ΩN → R defined as N (formula presented). j,k=1 We prove that fΩ is a Morse function for most domains Ω of class Cm+2,α, any m ≥ 0, 0 < α < 1. This applies in particular to the Robin function h : Ω → R, h(x) = HΩ(x, x), and to the Kirchhoff-Routh path function where Ω ⊂ R2, D = {x ∈ R2N : xj 6= xk for j 6= k}, and (formula presented).

The Morse property for functions of Kirchhoff-routh path type / Bartsch, T.; Micheletti, A. M.; Pistoia, A.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 12:7(2019), pp. 1867-1877. [10.3934/dcdss.2019123]

The Morse property for functions of Kirchhoff-routh path type

Bartsch T.;Micheletti A. M.;Pistoia A.
2019

Abstract

For a bounded domain Ω ⊂ Rn let HΩ : Ω ×Ω → R be the regular part of the Dirichlet Green function for the Laplace operator. Given a fixed arbitrary C2 function f : D → R, defined on an open subset D ⊂ RnN, and fixed coefficients λ1, . . ., λN ∈ R{0} we consider the function fΩ: D∩ΩN → R defined as N (formula presented). j,k=1 We prove that fΩ is a Morse function for most domains Ω of class Cm+2,α, any m ≥ 0, 0 < α < 1. This applies in particular to the Robin function h : Ω → R, h(x) = HΩ(x, x), and to the Kirchhoff-Routh path function where Ω ⊂ R2, D = {x ∈ R2N : xj 6= xk for j 6= k}, and (formula presented).
2019
Kirchhoff-Routh path function; Morse function; Transversality theorem
01 Pubblicazione su rivista::01a Articolo in rivista
The Morse property for functions of Kirchhoff-routh path type / Bartsch, T.; Micheletti, A. M.; Pistoia, A.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 12:7(2019), pp. 1867-1877. [10.3934/dcdss.2019123]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1466930
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