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On the Orlicz-Sobolev imbedding theorem. (English) Zbl 0344.46077

MSC:
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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Full Text: DOI
References:
[1] Adams, R. A.: Capacity and compact imbeddings. J. math. Mech. 19, 923-929 (1970) · Zbl 0193.41402
[2] Adams, R. A.: Sobolev spaces. (1975) · Zbl 0314.46030
[3] Adams, R. A.; Fournier, J.: Some imbedding theorems for Sobolev spaces. Canad. J. Math. 23, 517-530 (1971) · Zbl 0201.16301
[4] Cahill, I. G.: Compactness of Orlicz-Sobolev space imbeddings for unbounded domains. Master’s thesis (1975)
[5] Donaldson, T. K.; Trudinger, N. S.: Orlicz-Sobolev spaces and imbedding theorems. J. functional analysis 8, 52-75 (1971) · Zbl 0216.15702
[6] Gagliardo, E.: Proprietà di alcune classi di funzioni in più variabili. Ricerche mat. 7, 102-137 (1958) · Zbl 0089.09401
[7] Hempel, J. A.; Morris, G. R.; Trudinger, N. S.: On the sharpness of a limiting case of the Sobolev imbedding theorem. Bull. austral. Math. soc. 3, 369-373 (1970) · Zbl 0205.12801
[8] Krasnosel’skii, M. A.; Rutickii, Ya.B: Convex functions and Orlicz spaces. (1961)
[9] Luxemburg, W.: Banach function spaces. Thesis (1955) · Zbl 0068.09204
[10] Trudinger, N. S.: On imbeddings into Orlicz spaces and some applications. J. math. Mech. 17, 473-483 (1967) · Zbl 0163.36402