The Schwarz reflection principle for harmonic functions in R2 subject to the Robin condition

A non-local reflection formula for harmonic functions in R2 satisfying the Robin boundary condition, α∂nu+βu = 0, on a real-analytic curve is suggested. This formula generalizes the celebrated Schwarz reflection principle. It is also shown how the obtained formula reduces to well-known point-to-point reflection laws corresponding the Dirichlet and Neumann boundary conditions when one of the coefficients, α or β, vanishes