On the Modulus of Continuity of Weakly Differentiable Functions

Optimal embeddings of Sobolev type spaces into spaces of continuous functions are established. On extending the classical Morrey embedding on the Holder continuity of functions with weak derivatives in suitable Lebesgue spaces, our results provide the sharp modulus of continuity of functions whose weak derivatives of a given order belong to a more general rearrangement invariant space. In particular, embeddings of Orlicz-Sobolev spaces into spaces of continuous functions are characterized.