A modified Rayleigh conjecture for static problems

A modified Rayleigh conjecture (MRC) in scattering theory was proposed and justified by the author [A.G. Ramm, Modified Rayleigh conjecture and applications, J. Phys. A 35 (2002) L357-L361]. The MRC allows one to develop efficient numerical algorithms for solving boundary-value problems. It gives an error estimate for solutions. In this paper the MRC is formulated and proved for static problems.