Functions of class $C^1$ subject to a Legendre condition in an enhanced density set | Zendy

Silvano Delladio | Zendy

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Functions of class $C^1$ subject to a Legendre condition in an enhanced density set

Author(s) -

Silvano Delladio

Publication year - 2012

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/670

Subject(s) - class (philosophy) , subject (documents) , legendre polynomials , set (abstract data type) , mathematics , mathematical analysis , computer science , artificial intelligence , library science , programming language

We investigate certain second-order differential properties of functions and forms of class C at the points around which a suitable Legendrian condition is “very densely verified”. In particular we provide a generalization of the classical identity d = 0 on differential forms and some results about second-order osculating properties of graphs. Particular emphasis is placed on the case when the condition is verified in a locally finite perimeter set. A conjecture about the C-rectifiability of the horizontal projection of a Legendrian rectifiable set is discussed.

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