The Doubly Periodic "Jump" Problem for a Second-Order Linear Elliptic Equation With Constant Coefficients

For a homogeneous differential second-order equation of elliptic type with constant coefficients, we study the boundary-value problem of finding doubly periodic solutions for given jumps of the solutions themselves and their derivatives on a smooth as well as on a non-rectifiable closed contour. We get the necessary and sufficient conditions for the solvability of the problem and obtain explicit formulas for its solution.