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Because of the local nature of the boundary Harnack principle, we may assume that D is above the graph of a β-H¨older continuous function ϕ in Rn−1 . We may assume that ϕ ∞ 1 and ϕ(x) = 0 for |x| 1. For a point x ∈ D we define d(x) = xn − ϕ(x ), where x = (x , xn ). Let x0 be high above from the boundary. Suppose x is just below x0 and 0 < d(x) < 1. In general, δD (x) ≈ d(x) does not hold. We can assert only that δD (x)β Ad(x). Considering the line segment connecting x and x0 , we obtain the following 28 H.

The issue is that, in the physical language, Hadamard’s elementary solution is a solution to the problem about a point source of oscillations of impulse type. Singularities of such a solution are described by distributions λ γ+ , Γ (λ + 1) γ = γ(t, x), x = (x1 , x2 , . . , xm ), grad γ γ=0 = 0, where γ = 0 is the equation of the wavefront (γ < 0 in front of the wave), Γ is the Γ -function, λ = −(m − 1)/2, and m is the number of spatial variables. λ γ+ m−3 If m 3 is odd, then goes to δ ( 2 ) (γ), where δ is the deltaΓ (λ + 1) function.

Leray (1978). L. Sobolev (1983). Left to right: R. A. G. N. N. Rozhkovskaya (1983). 16 Y. Reshetnyak In 1960, the Institute launched the Siberian Mathematical Journal. From 1966 the journal was translated into English and published in the USA by Plenum Publishing Corporation (now known as Springer). The journal made the latest research of Siberian mathematicians available to the international mathematical community. By 1962, the organizational structure of the Institute of Mathematics was complete: the departments were comprised of algebra and mathematical logic, analysis, the theory of partial differential equations, the theory of functions of a complex variable, geometry and topology, mathematical economics, cybernetics, theoretical physics and computational center.