The Doubly Periodic “Jump” Problem for a Second-Order Linear Elliptic Equation With Constant Coefficients
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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.
Key wordselliptic equation boundary value problem doubly periodic function
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