# American Institute of Mathematical Sciences

July  1995, 1(3): 347-369. doi: 10.3934/dcds.1995.1.347

## A characterization of variational convergence for segmentation problems

 1 Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy 2 Dipartimento di Elettronica per l'Automazione, Università di Brescia, 25060 Brescia, Italy

Received  November 1994 Published  May 1995

We characterize the $\Gamma$-convergence of one-dimensional integral functionals with bulk and jump-part energies, by means of a suitable convergence of the integrands.
Citation: Micol Amar, Andrea Braides. A characterization of variational convergence for segmentation problems. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 347-369. doi: 10.3934/dcds.1995.1.347
 [1] Dominik Hafemeyer, Florian Mannel, Ira Neitzel, Boris Vexler. Finite element error estimates for one-dimensional elliptic optimal control by BV-functions. Mathematical Control and Related Fields, 2020, 10 (2) : 333-363. doi: 10.3934/mcrf.2019041 [2] Stefano Bianchini, Daniela Tonon. A decomposition theorem for $BV$ functions. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1549-1566. doi: 10.3934/cpaa.2011.10.1549 [3] Harun Karsli, Purshottam Narain Agrawal. Rate of convergence of Stancu type modified $q$-Gamma operators for functions with derivatives of bounded variation. Mathematical Foundations of Computing, 2022  doi: 10.3934/mfc.2022002 [4] Julián Fernández Bonder, Analía Silva, Juan F. Spedaletti. Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2125-2140. doi: 10.3934/dcds.2020355 [5] Gianni Dal Maso. Ennio De Giorgi and $\mathbf\Gamma$-convergence. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1017-1021. doi: 10.3934/dcds.2011.31.1017 [6] Alexander Mielke. Deriving amplitude equations via evolutionary $\Gamma$-convergence. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2679-2700. doi: 10.3934/dcds.2015.35.2679 [7] Kanghui Guo and Demetrio Labate. Sparse shearlet representation of Fourier integral operators. Electronic Research Announcements, 2007, 14: 7-19. doi: 10.3934/era.2007.14.7 [8] Joshua Du, Jun Ji. An integral representation of the determinant of a matrix and its applications. Conference Publications, 2005, 2005 (Special) : 225-232. doi: 10.3934/proc.2005.2005.225 [9] Gregory Beylkin, Lucas Monzón. Efficient representation and accurate evaluation of oscillatory integrals and functions. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4077-4100. doi: 10.3934/dcds.2016.36.4077 [10] Sylvia Serfaty. Gamma-convergence of gradient flows on Hilbert and metric spaces and applications. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1427-1451. doi: 10.3934/dcds.2011.31.1427 [11] Antonio De Rosa, Domenico Angelo La Manna. A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties. Communications on Pure and Applied Analysis, 2021, 20 (5) : 2101-2116. doi: 10.3934/cpaa.2021059 [12] Lorenza D'Elia. $\Gamma$-convergence of quadratic functionals with non uniformly elliptic conductivity matrices. Networks and Heterogeneous Media, 2022, 17 (1) : 15-45. doi: 10.3934/nhm.2021022 [13] Corrado Mascia. Stability analysis for linear heat conduction with memory kernels described by Gamma functions. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3569-3584. doi: 10.3934/dcds.2015.35.3569 [14] Pavel Krejčí, Harbir Lamba, Sergey Melnik, Dmitrii Rachinskii. Kurzweil integral representation of interacting Prandtl-Ishlinskii operators. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 2949-2965. doi: 10.3934/dcdsb.2015.20.2949 [15] Feng Qi, Bai-Ni Guo. Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1975-1989. doi: 10.3934/cpaa.2009.8.1975 [16] Jagannathan Gomatam, Isobel McFarlane. Generalisation of the Mandelbrot set to integral functions of quaternions. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 107-116. doi: 10.3934/dcds.1999.5.107 [17] Davide Addona, Giorgio Menegatti, Michele Miranda jr.. $BV$ functions on open domains: the Wiener case and a Fomin differentiable case. Communications on Pure and Applied Analysis, 2020, 19 (5) : 2679-2711. doi: 10.3934/cpaa.2020117 [18] Evelyn Herberg, Michael Hinze. Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022013 [19] Jian Zhai, Zhihui Cai. $\Gamma$-convergence with Dirichlet boundary condition and Landau-Lifshitz functional for thin film. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 1071-1085. doi: 10.3934/dcdsb.2009.11.1071 [20] Katsukuni Nakagawa. Compactness of transfer operators and spectral representation of Ruelle zeta functions for super-continuous functions. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6331-6350. doi: 10.3934/dcds.2020282

2020 Impact Factor: 1.392