On the existence of boundary values of solutions to an elliptic equation in a strip

A study was conducted to investigate the existence of boundary values of solutions to an elliptic equation in a strip. Condition (a) in the theorem revealed that the set of traces of the solution on straight lines parallel to the boundary was bounded. Investigations revealed that the existence conditions for L2-limits of the solution on the boundary depended on neither the equation degree nor its coefficients. Condition (a) was also necessary and sufficient for the existence of L2-limits of the solution on the boundary when equation (1) was of the second order. It was found that conditions (a) and (b) imposed on the solution were necessary and sufficient for the existence of L2-limits on the boundary in equation (1) and another equation. It was also demonstrated that the theorem was suitable for finding solutions to the more general elliptic equation.