n-Widths of Sobolev spaces inL p

LetW _p ^(r) ={f:f∈C ^r?1[0, 1],f ^(r?1) abs.cont., ∥f ^(r)∥ _p <∞}, and setB _p ^(r) ={f:f∈W _p ^(r) ,∥f ^(r)∥ _p ≤1}. We find the exact Kolmogorov, Gel'fand, linear, and Bernsteinn-widths ofB _p ^(r) inL ^p for allp∈(1, ∞). For the Kolmogorovn-width we show that forn≥r there exists an optimal subspace of splines of degreer?1 withn?r fixed simple knots depending onp.