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definition. Lipschitz bound [hart1996sphere, def. 3] [ag-000P]

A function \(f: \mathbb {R}^3 \rightarrow \mathbb {R}\) is Lipschitz over a domain \(D\) if and only if for all \(\boldsymbol {x}, \boldsymbol {y} \in D\), there exists a positive finite constant \(\lambda \), called Lipschitz bound, such that \[ |f(\boldsymbol {x})-f(\boldsymbol {y})| \leq \lambda \lVert \boldsymbol {x}-\boldsymbol {y}\rVert . \] The Lipschitz constant, denoted \(\operatorname {Lip} f\), is the minimum \(\lambda \) satisfying the condition above.