Geodesic
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
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 307-314 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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).
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).
Classification : 34A47, 34B15, 34C11, 46E35
Keywords: trace theory; anisotropic Sobolev spaces 
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     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Weidemaier, Peter. 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. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 307-314. http://geodesic.mathdoc.fr/item/CMUC_1991_32_2_a12/

[A] Adams R.A.: Sobolev Spaces. New York - San Francisco - London: Academic Press 1975. | MR | Zbl

[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

[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

[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

[K/J/F] Kufner A., John O., Fučik S.: Function Spaces. Leyden, Noordhoff Int. Publ. 1977. | MR

[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.

[R] Rákosník J.: Some remarks to anisotropic Sobolev spaces. I. Beiträge zur Analysis 13 (1979), 55-68. | MR

[W] Weidemaier P.: Local existence for parabolic problems with fully nonlinear boundary condition; an $L^p$-approach. to appear in Ann. mat. pura appl.

[W/Z] Wheeden R. L., Zygmund A.: Measure and Integral. New York - Basel: Dekker 1977. | MR | Zbl