“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php modified boundary conditions: (2.3) σ 12 (t, 0) = γ 0 u 2,111 (t, 0), t ∈ L 0 , u 2,1 (t, 0) = g 2 (t), t ∈ L 0 , in the contact zone, and (2.4) σ 12 (t, 0) = γ 1 u 2,111 (t, 0), t ∈ L 1 , σ 22 (t, 0) = −γ 2 u 2,11 (t, 0), t ∈ L 1 , outside of the contact zone, where σ 22 , σ 12 are the normal and the shear stresses acting on the boundary of the semiplane, the subindex 1 after the comma means differentiation by x, and g 2 (t) is the derivative of the function which describes the vertical profile of the rigid stamp. The coefficients γ 0 and γ 1 are allowed to have, in general, different values.…”