Gene

Quantum mechanics

Function (biology)

Pure mathematics

Biology

Laplace operator

Constant coefficients

Dimension (graph theory)

Eigenvalues and eigenvectors

Discontinuity (linguistics)

Biochemistry

Evolutionary biology

Physics

Mathematics

Laplace transform

Eigenfunction

Smoothness

Transcription factor

Mathematical analysis

Repressor

Chemistry

Operator (biology)

Piecewise

Journal of Physics Conference Series

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.

On the Localization Principle for Laplace Operator with Piecewise Constant Coefficient in Domains without Discontinuity Points