Extension of smooth functions from finitely connected planar domains

被引：0
作者：
Nahum Zobin
机构：
[1] College of William and Mary,Department of Mathematics
来源：
The Journal of Geometric Analysis | 1999年 / 9卷 / 3期
关键词：
46E35; extension of smooth functions; Whitney’s theorem; intrinsic metric;
D O I：
10.1007/BF02921985
中图分类号：
学科分类号：
摘要：
Consider the Sobolev space W∞k(Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions from W∞k(Ω) to the whole ℝ2 with preservation of class, i.e., surjectivity of the restriction operator W∞k(ℝ2) → W∞k(Ω).
引用
收藏
页码：491 / 511
页数：20
相关论文
共 13 条
  • [1] Calderón A.P.(1961)Lebesgue spaces of differentiable functions and distributions Proc. Symp. Pure Math. IV 33-49
  • [2] Gol’dshtein V.M.(1979)Criteria for extension of functions of the class L Siber. Math. J. 20 298-301
  • [3] Latfullin T.G.(1979) from unbounded plain domains Russian Math. Surveys 34 19-74
  • [4] Vodop’yanov S.K.(1981)On geometric properties of functions with generalized first derivatives Acta Math. 147 71-88
  • [5] Gol’dshtein V.M.(1987)Quasiconformal mappings and extendability of functions in Sobolev spaces Soviet Math. Dokl. 34 27-29
  • [6] Reshetnyak Yu.G.(1934)Criteria for the extension of Sobolev spaces W Trans. Am. Math. Soc. 36 63-89
  • [7] Vodop’yanov S.K.(1934)(Ω) for bounded plane domains Ann. Math. 35 482-485
  • [8] Jones P.W.(1995)Analytic extensions of differentiable functions defined in closed sets C.R. Acad. Sci. Paris 320 781-786
  • [9] Konovalov V.N.(1998)Functions differentiable on the boundaries of regions Adv. Math. 133 96-132
  • [10] Whitney H.(undefined)Whitney’s problem: extendability of functions and intrinsic metric undefined undefined undefined-undefined
12