Sobolev spaces | Operator theory

Trace operator

In mathematics, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev space. This is particularly important for the study of partial differential equations with prescribed boundary conditions (boundary value problems), where weak solutions may not be regular enough to satisfy the boundary conditions in the classical sense of functions. (Wikipedia).

Trace operator
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Topological manifold | Nuclear operators between Banach spaces | Continuous linear extension | Closure (topology) | Riesz representation theorem | Sobolev inequality | Kernel (linear algebra) | Sobolev space | Hölder condition | Divergence theorem | Divergence | Isomorphism theorems | Quotient space (linear algebra) | Boundary value problem | Dense set | Mathematics | Lipschitz continuity | Trace operator | Trace class | Weak solution | Poisson's equation | Domain (mathematical analysis) | Partial differential equation | Vector field | Image (mathematics)