Real functions Limits and continuity Concept
Lipschitz condition
Summary
A function satisfies a Lipschitz condition when the distance between two values is at most a constant times the distance between the two points. This is a strong form of continuity. In the theory of differential equations, it gives uniqueness of solutions. See the definition.
Remarks
It is named after Rudolf Lipschitz.
Where this leads
22 pages build on this one.
- Nonlinear Volterra equation
- Newton–Kantorovich theorem
- Hopf–Lax formula
- Kirszbraun theorem
- Cauchy integral on Lipschitz curves
- Portmanteau theorem
- Inertial manifold
- Admissible control
- Lipschitz domain
- Optimal control
- Talagrand's concentration inequality
- Broyden's method
- Contraction mapping principle for integral equations
- Backward Euler method
- McShane–Whitney extension
- Clarke generalized gradient
- Coarea formula
- Control system
- Kantorovich–Rubinstein duality
- Stochastic differential equation
- Local truncation error
- Input-to-state stability
Further reading
- Web https://en.wikipedia.org/wiki/Lipschitz_continuity, lead section
About this page
| Tag | 0AW1E6YTJY |
|---|---|
| URI | m2://0AW1E6YTJY |
| Aliases | lipschitz-continuity |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26A16 |
| Specializes | Uniform continuity |
| Same as |
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What links here
Definitions
Used by
- Nonlinear Volterra equation
- Newton–Kantorovich theorem
- Hopf–Lax formula
- Kirszbraun theorem
- Cauchy integral on Lipschitz curves
- Portmanteau theorem
- Inertial manifold
- Lipschitz domain
- Talagrand's concentration inequality
- Broyden's method
- Contraction mapping principle for integral equations
- Backward Euler method
- McShane–Whitney extension
- Clarke generalized gradient
- Coarea formula
- Control system
- Kantorovich–Rubinstein duality
- Stochastic differential equation
- Local truncation error
- Input-to-state stability