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Keywords:
weighted Sobolev spaces; Poincaré inequality
weighted Sobolev spaces; Poincaré inequality
Summary:
We give necessary and sufficient conditions for the equality $H=W$ in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.
References:
[1] Chua S.-K.: Extension theorems on weighted Sobolev spaces. Indiana Univ. Math. J. (1992), 41 1027-1076. MR 1206339 | Zbl 0767.46025
[2] Deny J., Lions J.L.: Les espaces du type de Beppo Levi. Ann. Inst. Fourier 5 (1953-54), 305-370. MR 0074787 | Zbl 0065.09903
[3] Evans L.C., Gariepy R.R.: Measure Theory and Fine Properties of Functions. CRC Press Boca Raton (1992). MR 1158660 | Zbl 0804.28001
[4] Fabes E.B., Kenig C.E., Serapioni R.P.: The local regularity of solutions of degenerate elliptic equations. Comm. P.D.E. 7 (1982), 77-116. MR 0643158 | Zbl 0498.35042
[5] Hajłasz P.: Sobolev spaces on an arbitrary metric space. Potential Analysis 5 (1996), 403-415. MR 1401074
[6] Hajłasz P., Koskela P.: Sobolev meets Poincaré. C.R. Acad. Sci. Paris Sér. I (1995), 320 1211-1215. MR 1336257
[7] Heinonen J., Kilpeläinen T., Martio O.: Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford University Press Oxford (1993). MR 1207810
[8] Heinonen J., Koskela P.: Weighted Sobolev and Poincaré inequalities and quasiregular mappings of polynomial type. Math. Scand. 77 (1995), 251-271. MR 1379269 | Zbl 0860.30018
[9] Kilpeläinen T.: Weighted Sobolev spaces and capacity. Ann. Acad. Sci. Fenn. Ser. A I. Math. 19 (1994), 95-113. MR 1246890
[10] Kufner A.: Weighted Sobolev Spaces. Wiley New York (1985). MR 0802206 | Zbl 0579.35021
[11] Kufner A., Opic B.: How to define reasonably weighted Sobolev spaces. Comment. Math. Univ. Carol. 25 (1984), 537-554. MR 0775568 | Zbl 0557.46025
[12] Liu F.-C.: A Lusin type property of Sobolev functions. Indiana Univ. Math. J. 26 (1977), 645-651. MR 0450488
[13] Meyers N., Serrin J.: $H=W$. Proc. Nat. Acad, Sci. USA 51 (1964), 1055-1056. MR 0164252 | Zbl 0123.30501
[14] Stein E.M.: Harmonic Analysis. Princeton University Press Princeton, New Jersey (1993). MR 1232192 | Zbl 0821.42001
[15] Turesson B.O.: Nonlinear potential theory and weighted Sobolev spaces. Thesis, University of Linköping, 1995. MR 1371571 | Zbl 0949.31006
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