Characterization of the variable exponent Sobolev norm without derivatives
Hästö, Peter; Ribeiro, Ana Margarida (2016-03-30)
Hästö, Peter
Ribeiro, Ana Margarida
World Scientific
30.03.2016
Hästö, P., Ribeiro, A. (2017) Characterization of the variable exponent Sobolev norm without derivatives. Communications in Contemporary Mathematics, 19 (03), 1650022. doi:10.1142/S021919971650022X
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Electronic version of an article published as Communications in Contemporary Mathematics, 19, 03, 2017, https://doi.org/10.1142/S021919971650022X © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ccm.
https://rightsstatements.org/vocab/InC/1.0/
Electronic version of an article published as Communications in Contemporary Mathematics, 19, 03, 2017, https://doi.org/10.1142/S021919971650022X © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ccm.
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2019040110638
https://urn.fi/URN:NBN:fi-fe2019040110638
Tiivistelmä
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.
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