| Title:
|
Smooth approximation in weighted Sobolev spaces (English) |
| Author:
|
Kilpeläinen, T. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
29-35 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
weighted Sobolev spaces |
| Keyword:
|
Poincaré inequality |
| MSC:
|
41A65 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0886.46035 |
| idMR:
|
MR1455468 |
| . |
| Date available:
|
2009-01-08T18:28:55Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118900 |
| . |
| Reference:
|
[1] Chua S.-K.: Extension theorems on weighted Sobolev spaces.Indiana Univ. Math. J. (1992), 41 1027-1076. Zbl 0767.46025, MR 1206339 |
| Reference:
|
[2] Deny J., Lions J.L.: Les espaces du type de Beppo Levi.Ann. Inst. Fourier 5 (1953-54), 305-370. Zbl 0065.09903, MR 0074787 |
| Reference:
|
[3] Evans L.C., Gariepy R.R.: Measure Theory and Fine Properties of Functions.CRC Press Boca Raton (1992). Zbl 0804.28001, MR 1158660 |
| Reference:
|
[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. Zbl 0498.35042, MR 0643158 |
| Reference:
|
[5] Hajłasz P.: Sobolev spaces on an arbitrary metric space.Potential Analysis 5 (1996), 403-415. MR 1401074 |
| Reference:
|
[6] Hajłasz P., Koskela P.: Sobolev meets Poincaré.C.R. Acad. Sci. Paris Sér. I (1995), 320 1211-1215. MR 1336257 |
| Reference:
|
[7] Heinonen J., Kilpeläinen T., Martio O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.Oxford University Press Oxford (1993). MR 1207810 |
| Reference:
|
[8] Heinonen J., Koskela P.: Weighted Sobolev and Poincaré inequalities and quasiregular mappings of polynomial type.Math. Scand. 77 (1995), 251-271. Zbl 0860.30018, MR 1379269 |
| Reference:
|
[9] Kilpeläinen T.: Weighted Sobolev spaces and capacity.Ann. Acad. Sci. Fenn. Ser. A I. Math. 19 (1994), 95-113. MR 1246890 |
| Reference:
|
[10] Kufner A.: Weighted Sobolev Spaces.Wiley New York (1985). Zbl 0579.35021, MR 0802206 |
| Reference:
|
[11] Kufner A., Opic B.: How to define reasonably weighted Sobolev spaces.Comment. Math. Univ. Carol. 25 (1984), 537-554. Zbl 0557.46025, MR 0775568 |
| Reference:
|
[12] Liu F.-C.: A Lusin type property of Sobolev functions.Indiana Univ. Math. J. 26 (1977), 645-651. MR 0450488 |
| Reference:
|
[13] Meyers N., Serrin J.: $H=W$.Proc. Nat. Acad, Sci. USA 51 (1964), 1055-1056. Zbl 0123.30501, MR 0164252 |
| Reference:
|
[14] Stein E.M.: Harmonic Analysis.Princeton University Press Princeton, New Jersey (1993). Zbl 0821.42001, MR 1232192 |
| Reference:
|
[15] Turesson B.O.: Nonlinear potential theory and weighted Sobolev spaces.Thesis, University of Linköping, 1995. Zbl 0949.31006, MR 1371571 |
| . |
