
 
Fractional SobolevPoincaré Inequalities inIrregular Domains 
 
Citation： 
ChangYu GUO.Fractional SobolevPoincaré Inequalities inIrregular Domains[J].Chinese Annals of Mathematics B,2017,38(3):839~856 
Page view： 3275
Net amount： 3095 
Authors： 
ChangYu GUO; 
Foundation： 
This work was supported by the Magnus Ehrnrooth Foundation. 


Abstract： 
This paper is devoted to the study of fractional
$(q,p)$SobolevPoincar\'e inequalities in irregular domains. In
particular, the author establishes (essentially) sharp fractional
$(q,p)$SobolevPoincar\'e inequalities in $s$John domains and in
domains satisfying the quasihyperbolic boundary conditions. When the
order of the fractional derivative tends to 1, our results tend to
the results for the usual derivatives. Furthermore, the author
verifies that those domains which support the fractional
$(q,p)$SobolevPoincar\'e inequalities together with a separation
property are $s$diam John domains for certain $s$, depending only
on the associated data. An inaccurate statement in [Buckley, S. and
Koskela, P., SobolevPoincar\'e implies John, \textit{Math. Res.
Lett.}, \textbf{2}(5), 1995, 577593]is also pointed out. 
Keywords： 
Fractional SobolevPoincaré inequality, $s$John domain,
Quasihyperbolic boundary condition 
Classification： 
46E35, 26D10 

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