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58, No. I0, 142-152, (1929). S. L. Sobolev, "On certain theorems of functional analysis," Mat. , 4 (46), No. 3, 471-498 (1938). 6. 7. 8. 9. 95 V. G. Maz'ya i~ Basic Notation. ~ + ~'~ E ~ . with compact closure 0 be a point on the curve ~ ' ~ ~ , and , and suppose that We consider the elliptic operator 2 in ~'~ , where the be a subdomain of ~ 2 # 2 # G~j- are functions that satisfy a Lipschitz condition in a positive-definite matrix, and the a[ and ~ ~ and form are bounded measurable functions. Without loss of generality, we shall assume (except in Remark 2) that IIO~F(0)I I is the unit matrix.

Maz'ya, "On the continuity and boundedness of functions in S. L. Sobolev spaces," in: Problems of Mathematical Analysis, No. 4: Integral and Differential Operators,Differential Equations, J. Soy. Math. ~, No. 29-50 (1976). V. G. Maz'ya, "Classes of sets and measures that are connected with imbedding theorems," in: Imbedding Theorems and Their Applications, (Proceedings of a Symposium, Baku 1966), [in Russian], Nauka, Moscow (1970), pp. 142-159, 246. J. -L. Lions, "Spaces of the Beppo Levi type," Ann.

Fourier, ~, 305- 2. 3. 37O (1955). 5. V. G. Maz'ya, "On weak solutions of the Dirichlet and Neumann problems," Tr. Mosk. Mat. , 20, 137-172 (1969). V. G. Maz'ya, "On the Neumann problem in regions with nonregular boundaries," Sib. Mat. , ~, 1322-1350 (1968). E. Gagliardo, "Properties of certain classes of functions of several variables," Ricerche Mat. , No. I, 102-137 (1958). G. H. Hardy, J. E. Littlewood, and G. Polya, "Some simple inequalities satisfied by convex functions," Messenger Math. 58, No.

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