| Title:
|
The trace theorem $W^{2,1}_p(\Omega_T) \ni f \mapsto \nabla_{\!x} f \in W^{1-1/p,1/2-1/2p}_p(\partial \Omega_T)$ revisited (English) |
| Author:
|
Weidemaier, Peter |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
307-314 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Filling a possible gap in the literature, we give a complete and readable proof of this trace theorem, which also shows that the imbedding constant is uniformly bounded for $T \downarrow 0$. The proof is based on a version of Hardy's inequality (cp. Appendix). (English) |
| Keyword:
|
trace theory |
| Keyword:
|
anisotropic Sobolev spaces |
| MSC:
|
34A47 |
| MSC:
|
34B15 |
| MSC:
|
34C11 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0770.46018 |
| idMR:
|
MR1137792 |
| . |
| Date available:
|
2009-01-08T17:44:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116972 |
| . |
| Reference:
|
[A] Adams R.A.: Sobolev Spaces.New York - San Francisco - London: Academic Press 1975. Zbl 1098.46001, MR 0450957 |
| Reference:
|
[B/I/N] Besov O.V., Il'in V.P., Nikol'skii S.M.: Integral Representations of Functions and Imbedding Theorems, Vol. I..Wiley, 1978. Zbl 0392.46022 |
| Reference:
|
[I] Il'in V.P.: The properties of some classes of differentiable functions of several variables defined in an n-dimensional region.Transl. AMS 81 (1969), 91-256 Trudy Mat. Inst. Steklov 66 (1962), 227-363. MR 0153789 |
| Reference:
|
[I/S] Il'in V.P., Solonnikov V.A.: On some properties of differentiable functions of several variables.Transl. AMS 81 (1969), 67-90 Trudy Mat. Inst. Steklov 66 (1962), 205-226. MR 0152793 |
| Reference:
|
[K/J/F] Kufner A., John O., Fučik S.: Function Spaces.Leyden, Noordhoff Int. Publ. 1977. MR 0482102 |
| Reference:
|
[L/S/U] Ladyshenskaya O.A., Solonnikov V.A., Uralceva N.N: Linear and Quasilinear Equations of Parabolic Type.Am. Math. Soc., Providence, R.I. 1968. |
| Reference:
|
[R] Rákosník J.: Some remarks to anisotropic Sobolev spaces.I. Beiträge zur Analysis 13 (1979), 55-68. MR 0536217 |
| Reference:
|
[W] Weidemaier P.: Local existence for parabolic problems with fully nonlinear boundary condition; an $L^p$-approach.to appear in Ann. mat. pura appl. |
| Reference:
|
[W/Z] Wheeden R. L., Zygmund A.: Measure and Integral..New York - Basel: Dekker 1977. Zbl 0362.26004, MR 0492146 |
| . |
