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Generalization of p-regularity notion and tangent cone description in the singular case

Wiesław GrzegorczykBeata MedakAlexey A. Tret’yakov — 2012

Annales UMCS, Mathematica

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.

Generalization of p-regularity notion and tangent cone description in the singular case

Wiesław GrzegorczykBeata MedakAlexey A. Tret’yakov — 2012

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.

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