On the Localization Principle for Laplace Operator with Piecewise Constant Coefficient in Domains without Discontinuity Points
M. Suchkov, V P Trifonenkov · Journal of Physics Conference Series · 2017
Some properties of spectral expansions that correspond to eigenfunction system of Laplace operator with discontinuous coefficient are studied. The authors prove that for the case of arbitrary domains of dimension N = 2 or N = 3, localization principle in domains without discontinuity points is preserved despite the discontinuity of the coefficient. If N ≥ 5, then localization principle is violated in points located "far" from the surface of discontinuity of the coefficient, even in case of infinite smoothness of expanded function.