| Title:
|
A second look on definition and equivalent norms of Sobolev spaces (English) |
| Author:
|
Naumann, J. |
| Author:
|
Simader, C. G. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
315-328 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sobolev's original definition of his spaces $L^{m,p}(\Omega)$ is revisited. It only assumed that $\Omega\subseteq\Bbb R^n$ is a domain. With elementary methods, essentially based on Poincare's inequality for balls (or cubes), the existence of intermediate derivates of functions $u\in L^{m,p}(\Omega)$ with respect to appropriate norms, and equivalence of these norms is proved. (English) |
| Keyword:
|
Sobolev spaces |
| Keyword:
|
Poincaré’s inequality |
| Keyword:
|
existence of intermediate derivates |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0941.46019 |
| idMR:
|
MR1780700 |
| DOI:
|
10.21136/MB.1999.126243 |
| . |
| Date available:
|
2009-09-24T21:38:29Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126243 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Burenkov V. I.: Sobolev Spaces on Domains.B. G. Teubner, Stuttgart, 1998. Zbl 0893.46024, MR 1622690 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[б] Maz'ja V. G.: Sobolev Spaces.Springer-Verlag, Berlin, 1985. Zbl 0692.46023, MR 0817985 |
| Reference:
|
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| Reference:
|
[8] Nečas J.: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[9] Nikoľskij S. M.: Approximation of Functions of Several Variables and Imbedding Theorems.Engl. transl: Springer-Verlag, Berlin 1975, Izd. Nauka, Moskva, 1969 (In Russian.). MR 0374877 |
| Reference:
|
[10] Sobolev S. L.: On some estimates related to families of functions having derivatives which are square integrable.Dokl. Akad. Nauk 1 (1936), 267-270. (In Russian.) |
| Reference:
|
[11] Sobolev S. L.: On a theorem in functional analysis.Mat. Sborn. 4 (1938), 471-497 (In Russian.); Engl. transl. Amer. Math. Soc. Transl. II Ser. 34 (1963), 39-68. |
| Reference:
|
[12] Sobolev S. L.: Some Applications of Functional Analysis in Mathematical Physics.1st ed.: LGU Leningrad, 1950; 2nd ed.: NGU Novosibirsk, 1962; Зrd ed.; Izd. Nauka, Moskva 1988. (In Russian.) Engl. transl.: Amer. Math. Soc. Providence R.I, 1963; German transl: Akademie-Verlag Berlin 1964. MR 0986735 |
| Reference:
|
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| Reference:
|
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| . |
