標題: On a generalization of L-p-differentiability
作者: Spector, Daniel
應用數學系
Department of Applied Mathematics
公開日期: Jun-2016
摘要: In this paper we connect Calderon and Zygmund\'s notion of L-p-differentiability (Calderon and Zygmund, Proc Natl Acad Sci USA 46: 1385-1389, 1960) with some recent characterizations of Sobolev spaces via the asymptotics of non-local functionals due to Bourgain, Brezis, and Mironescu (Optimal Control and Partial Differential Equations, pp. 439-455, 2001). We showhowthe results of the former can be generalized to the setting of the latter, while the latter results can be strengthened in the spirit of the former. As a consequence of these results we give several new characterizations of Sobolev spaces, a novel condition for whether a function of bounded variation is in the Sobolev space W-1,W-1, and complete the proof of a characterization of the Sobolev spaces recently claimed in (Leoni and Spector, J Funct Anal 261: 2926-2958, 2011; Leoni and Spector, J Funct Anal 266: 1106-1114, 2014).
URI: http://dx.doi.org/10.1007/s00526-016-1004-9
http://hdl.handle.net/11536/133953
ISSN: 0944-2669
DOI: 10.1007/s00526-016-1004-9
期刊: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume: 55
Issue: 3
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