A1 Refereed original research article in a scientific journal
Characterization of the variable exponent Sobolev norm without derivatives
Authors: Peter Hästö, Ana Margarida Ribeiro
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Publication year: 2017
Journal: Communications in Contemporary Mathematics
Journal name in source: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
Journal acronym: COMMUN CONTEMP MATH
Article number: ARTN 1650022
Volume: 19
Issue: 3
Number of pages: 13
ISSN: 0219-1997
eISSN: 1793-6683
DOI: https://doi.org/10.1142/S021919971650022X
Abstract
The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space.
The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space.
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