Abstract
We consider the question of uniqueness for the solutions of the boundary value problem urn:x-wiley:0025584X:mana19861250115:equation:mana19861250115-math-0001 where sgn K(y) = sgn y and Γ0 and Γ1 are parts of the boundary of a bounded simply connected region G in R2. G is bounded for y > 0 by a piecewise smooth curve Γ0 which intersects the line y = 0 at A (– 1, 0) and B(0, 0). For y < 0 G is bounded by a piecewise smooth curve Γ1 through A, which meets the characteristic of (1) issued from B at point C, and by the curve Γ2 which consists of the portion CB of the characteristic through B.Using energy‐integral considerations, we give sufficient conditions for the uniqueness of solutions to boundary value problem (1).
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