Gelfand numbers of embeddings of mixed Besov spaces

Let Sp1,p1tB((0,1)d) be the Besov spaces with dominating mixed smoothness on (0,1)d. In this paper we consider the problem App:Sp1,p1tB((0,1)d)→Lp2((0,1)d) and investigate the asymptotic behaviour of Gelfand numbers of this embedding. We shall give the correct order of convergence of Gelfand numbers in almost all cases. In addition we shall compare these results with the known behaviour of approximation numbers.