Stable Regular Critical Points of the Mumford-shah Functional Are Local Minimizers

نویسنده

  • M. BONACINI
چکیده

In this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the L1 -topology.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some remarks on the analyticity of minimizers of free discontinuity problems

In this paper we give a partial answer to a conjecture of De Giorgi, namely we prove that in dimension two the regular part of the discontinuity set of a local minimizer of the homogeneous Mumford-Shah functional is analytic with the exception of at most a countable number of isolated points.

متن کامل

Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets

Using a calibration method, we prove that, if w is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional open set Ω, and the discontinuity set of w is a segment connecting two boundary points, then for every point (x0, y0) of Ω there exists a neighbourhood U of (x0, y0) such that w is a minimizer of the Mumford-Shah functional on U with respect to ...

متن کامل

DENSITY LOWER BOUND ESTIMATES FOR LOCAL MINIMIZERS OF THE 2d MUMFORD-SHAH ENERGY

We prove, using direct variational arguments, an explicit energy-treshold criterion for regular points of 2-dimensional Mumford-Shah energy minimizers. From this we infer an explicit constant for the density lower bound of De Giorgi, Carriero and Leaci.

متن کامل

Higher Integrability for Minimizers of the Mumford-shah Functional

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].

متن کامل

Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set

Using a calibration method, we prove that, if w is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional open set Ω, and the discontinuity set Sw of w is a regular curve connecting two boundary points, then there exists a uniform neighbourhood U of Sw such that w is a minimizer of the Mumford-Shah functional on U with respect to its own boundary co...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013