An Example on Sobolev Space Approximation

For each d2 we construct a connected open set R^d such that = int (clos()), and for each k 1 and each p 1, ), the subsetW^k, () fails to be dense in the Sobolev space W^{k, p}(), in thenorm of W^{k, p}(). 1991 Mathematics Subject Classification 46E35,46F05.