Reunafunktio

Reunafunktio is a Finnish term roughly translating to "boundary function" or "edge function." In Finnish mathematical and technical literature it is used to denote a function that is associated with the boundary of a geometric object, domain, or region. The exact interpretation of the term varies by context, and it is not universally standardized in English-language mathematics.

In the context of partial differential equations, reunafunktio commonly refers to a function defined on the boundary ∂Ω of a domain Ω that specifies boundary conditions for a solution. For example, a Dirichlet reunafunktio prescribes the values of the solution on the boundary, while a Neumann reunafunktio prescribes the normal derivative. Another frequent interpretation is as a boundary indicator or distance-to-boundary function, which measures proximity to the boundary and is used in applications such as mesh generation and level-set methods.

In image processing and computer vision, the concept may appear as an edge-related function used to detect or enhance boundaries within an image, though this usage is less standardized in Finnish terminology. Reunafunktio as a term thus spans both mathematical boundary data and boundary-related measures in applied contexts.

See also: boundary, boundary value problem, Dirichlet problem, Neumann problem, indicator function, distance-to-boundary function.