Boundedness of solutions to Dirichlet problems for fully anisotropic elliptic equations

A necessary and sucient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into L1(Rn) is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to be continuous. Improvements of this result are also oered. They provide the optimal Orlicz target space, and the optimal rearrangement-invariant target space in the embedding in question. These results complement those already available in the subcritical case, where the embedding into L1(Rn) fails. They also augment a classical embedding theorem for standard fractional Sobolev spaces.