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In mathematics, a coercive function is a function that "grows rapidly" at the extremes of the space on which it is defined. More precisely, a function f : Rn → Rn is called coercive if
where "" denotes the usual dot product and "| u |" denotes the usual Euclidean norm of the vector u.
More generally, a function f : X → Y between two topological spacesX and Y is called coercive if, for every compact subsetJ of Y there exists a compact subset K of X such that
References
Renardy, Michael and Rogers, Robert C. (2004). An introduction to partial differential equations (Second edition ed.). New York, NY: Springer-Verlag. pp. xiv+434. ISBN 0-387-00444-0. {{cite book}}: |edition= has extra text (help)CS1 maint: multiple names: authors list (link)
