Functional analysis Distributions and generalized functions Concept
Weak derivative
Summary
A weak derivative of a locally integrable function is a function that obeys the integration by parts formula against all smooth compactly supported test functions. It agrees with the usual partial derivative for continuously differentiable functions, but it also exists for many functions with corners. Weak derivatives are used to define Sobolev spaces and weak solutions of partial differential equations.
Where this leads
18 pages build on this one.
- Elliptic regularity
- Céa's lemma
- Vanishing mean oscillation
- Gagliardo–Nirenberg interpolation inequality
- Fredholm property of elliptic operators
- Lax–Milgram theorem
- Minimum total potential energy principle
- Sobolev inequality
- Sobolev space
- Hardy–Littlewood–Sobolev inequality
- Poincaré inequality
- Bramble–Hilbert lemma
- Galerkin method
- p-harmonic function
- Weak solution
- Ladyzhenskaya–Babuška–Brezzi condition
- Rellich–Kondrachov theorem
- Morrey's inequality
Further reading
About this page
| Tag | C3EC148VZD |
|---|---|
| URI | m2://C3EC148VZD |
| Kind | concept |
| Writing | W0 stub |
| MSC | 46E35, 35D30, 46F10 |
| Same as |
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Used by
- Elliptic regularity
- Gagliardo–Nirenberg interpolation inequality
- Sobolev inequality
- Sobolev space
- Bramble–Hilbert lemma
- p-harmonic function
- Weak solution