We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi [5].

We derive the asymptotic behaviour of the one point probability density for the inhomogeneous shock slopes in the turbulent regime, when a Gaussian fluctuating flux at origin derives the system. We also calculate the time dependence of the xf beyond which there won’t exist any velocity shocks as xf ∼= t3/4(log t)1/4. We argue that the stationary state of the problem would be equivalent with the...

We prove that a certain series defines a constant function using Wolpert’s formula for the variation of the length of a geodesic along a Fenchel Nielsen twist. Subsequently we determine the value viewing it as function on the the Deligne Mumford compactification M1,1 and evaluating it at the stable curve at infinity. Conventions: 1. For γ an essential closed curve on a surface lγ(x) is the leng...

We compute explicitly the anisotropy eeect in the H 1 term, generated in the approximation of the Mumford-Shah functional by nite element spaces deened on structured triangulations.

Two important aspects of the epidemiology of suicides in the elderly people can potentially be applied to dementia. The first is the well-established observation of the independent effects of age, birth cohort membership, and the period on the risk of suicide in the elderly people (Murphy et al., 1986; Surtees and Duffy, 1989; Snowdon and Hunt, 2002). The second is the recently developed concep...

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We propose a variational approach for deblurring and impulsive noise removal in multi-channel images. A robust data fidelity measure and edge preserving regularization are employed. We consider several regularization approaches, such as Beltrami flow, Mumford-Shah and Total-Variation Mumford-Shah. The latter two methods are extended to multi-channel images and reformulated using the Γ -converge...