On sharp condition for imbedding anisotropic Sobolev-Orlicz spaces in a space of continuous functions (Q1206264)

Let \(G\subset R^ n\) be a open and bounded set and \(f = (f_ 1, \dots, f_ n)\), where \(f_ i : [0, \infty) \to [0, \infty]\) is Young's function for \(i=1, \dots,n\). The author establishes necessary and sufficient conditions for imbedding anisotropic Sobolev-Orlicz space \({\overset \circ W}^ 1_ f (G)\) into the space of continuous and bounded functions. These results are the proceeding of the author's paper studying the imbedding of isotropic Sobolev-Orlicz spaces from [Mat. Zametki, 9, No. 6, 639-650 (1971; Zbl 0219.46028)].