Lipschitz metric for the modified two-component Camassa–Holm system

Lipschitz Metric for the Hunter–saxton Equation

We study stability of solutions of the Cauchy problem for the Hunter–Saxton equation ut + uux = 14 ( R x −∞ u 2 x dx− R∞ x ux dx) with initial data u0. In particular, we derive a new Lipschitz metric dD with the property that for two solutions u and v of the equation we have dD(u(t), v(t)) ≤ edD(u0, v0).

a study on construction of iranian life tables: the case study of modified brass logit system

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Metric Embeddings and Lipschitz Extensions

Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space

We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can be decomposed f into a finite number of BiLipschitz functions f |Fi so that the k-Hausdorff content of f([0, 1] r ∪Fi) is small. We thus generalize a theorem of P. Jones [Jon88] from the setting of R to the setting of a general metric spa...

Lipschitz Metric for the Periodic Camassa–holm Equation

We study stability of conservative solutions of the Cauchy problem for the periodic Camassa–Holm equation ut−uxxt +3uux−2uxuxx−uuxxx = 0 with initial data u0. In particular, we derive a new Lipschitz metric dD with the property that for two solutions u and v of the equation we have dD(u(t), v(t)) ≤ edD(u0, v0). The relationship between this metric and usual norms in H1 per and L ∞ per is clarif...