A class of extended real valued functionals, already considered for evolution problems, is studied. The set where the functional is finite is proved to be an absolute neighborhood extensor. Applications to critical point theory, involving Ljusternik-Schnirelman category and cohomological index, are shown. The stability under Γ-convergence of the homotopical type of the sublevels of the functional is also treated.
Degiovanni, M., Homotopical properties of a class of nonsmooth functions, <<ANNALI DI MATEMATICA PURA ED APPLICATA>>, 1990; 156 (1): 37-71. [doi:10.1007/BF01766973] [https://hdl.handle.net/10807/312968]
Homotopical properties of a class of nonsmooth functions
Degiovanni, Marco
Primo
Conceptualization
1990
Abstract
A class of extended real valued functionals, already considered for evolution problems, is studied. The set where the functional is finite is proved to be an absolute neighborhood extensor. Applications to critical point theory, involving Ljusternik-Schnirelman category and cohomological index, are shown. The stability under Γ-convergence of the homotopical type of the sublevels of the functional is also treated.
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