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Characterization of the variable exponent Sobolev norm without derivatives
Tekijät: Peter Hästö, Ana Margarida Ribeiro
Kustantaja: WORLD SCIENTIFIC PUBL CO PTE LTD
Julkaisuvuosi: 2017
Journal: Communications in Contemporary Mathematics
Tietokannassa oleva lehden nimi: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
Lehden akronyymi: COMMUN CONTEMP MATH
Artikkelin numero: ARTN 1650022
Vuosikerta: 19
Numero: 3
Sivujen määrä: 13
ISSN: 0219-1997
eISSN: 1793-6683
DOI: https://doi.org/10.1142/S021919971650022X
Tiivistelmä
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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