A remark on differentiable functions with partial derivatives in Lp

Cristina Di Bari, Calogero Vetro, Cristina Di Bari

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3 Citazioni (Scopus)

Abstract

We consider a definition of p, δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.
Lingua originaleEnglish
pagine (da-a)227-234
Numero di pagine8
RivistaJournal of Mathematical Analysis and Applications
Volume299
Stato di pubblicazionePublished - 2004

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Partial derivative
Differentiable
Derivatives
P-variation
Measurable set
Change of Variables
Several Variables
Differentiability
Integrability

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cita questo

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abstract = "We consider a definition of p, δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Mal{\'y} and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.",
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AU - Di Bari, Cristina

AU - Vetro, Calogero

AU - Di Bari, Cristina

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N2 - We consider a definition of p, δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

AB - We consider a definition of p, δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

UR - http://hdl.handle.net/10447/16702

M3 - Article

VL - 299

SP - 227

EP - 234

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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