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Orlicz-Sobolev spaces and imbedding theorems. (English) Zbl 0216.15702

MSC:
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30Spaces of measurable functions
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References:
[1] Clark, C. W.: Introduction to Sobolev spaces. Seminar notes (1968) · Zbl 0159.15701
[2] Dankert, G.: Sobolev imbedding theorems in Orlicz spaces. Thesis (1966)
[3] Donaldson, T. K.: Orlicz-Sobolev spaces and applications. (1969)
[4] T. K. Donaldson, Existence theorems for nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, to appear. · Zbl 0207.41501
[5] Dubinski, J. A.: Some imbedding theorems in Orlicz spaces. Dokl. akad. Nauk SSSR 152, 529-532 (1963)
[6] Krasnoselskii, M. A.; Rutickii, Y.: Convex functions and Orlicz spaces. (1961)
[7] Lions, J. L.: Problèmes aux limites dans LES équations aux derivées partielles. (1966)
[8] Meyers, N. G.; Serrin, J. B.: Revised ed. H = W, proc. Nat. acad. Sci. USA. H = W, proc. Nat. acad. Sci. USA 51, 1055-1056 (1964) · Zbl 0123.30501
[9] Morrey, C. B.: Multiple integral problems in the calculus of variations. (1966) · Zbl 0142.38701
[10] Neças, J.: LES méthodes directes en théorie des équations élliptiques. (1967)
[11] O’neill, R.: Fractional integration in Orlicz spaces. Trans. amer. Math. soc. 115, 300-328 (1965)
[12] Serrin, J. B.: Local behaviour of solutions of quasilinear equations. Acta math. 113, 219-240 (1965) · Zbl 0173.39202
[13] Spanne, S.: Some function spaces defined using the mean oscillation over cubes. Ann. sc. Norm. sup. Pisa 19, 593-608 (1965) · Zbl 0199.44303
[14] Trudinger, N. S.: On imbeddings into Orlicz spaces and applications. J. math. Mech. 17, 473-484 (1967) · Zbl 0163.36402
[15] N. S. Trudinger, Continuity of weak solutions of quasilinear equations, to appear. · Zbl 0883.35035
[16] Zaanen, A. C.: Linear analysis. (1953) · Zbl 0053.25601