Integral representation results are obtained for the relaxation of some classes of energy functionals depending on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical equilibrium problems.
Accepté le :
DOI : 10.1051/cocv/2016065
Mots-clés : Relaxation, convexity-quasiconvexity, functions of bounded variation
@article{COCV_2017__23_4_1555_0, author = {Carita, Gra\c{c}a and Zappale, Elvira}, title = {Integral representation results in $BV \times{} L^{p}$}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1555--1599}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016065}, zbl = {1381.49007}, mrnumber = {3716933}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016065/} }
TY - JOUR AU - Carita, Graça AU - Zappale, Elvira TI - Integral representation results in $BV \times{} L^{p}$ JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1555 EP - 1599 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016065/ DO - 10.1051/cocv/2016065 LA - en ID - COCV_2017__23_4_1555_0 ER -
%0 Journal Article %A Carita, Graça %A Zappale, Elvira %T Integral representation results in $BV \times{} L^{p}$ %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1555-1599 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016065/ %R 10.1051/cocv/2016065 %G en %F COCV_2017__23_4_1555_0
Carita, Graça; Zappale, Elvira. Integral representation results in $BV \times{} L^{p}$. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1555-1599. doi : 10.1051/cocv/2016065. http://archive.numdam.org/articles/10.1051/cocv/2016065/
Semicontinuity problems in the Calculus of variations. Arch. Rational Mech. Anal. 86 (1984) 125–145. | DOI | MR | Zbl
and ,Rank one property for derivatives of functions with bounded variation. Proc. R. Soc. Edinb. Sect. A 123 (1993) 239–274. | DOI | MR | Zbl
,On the Relaxation in of Quasi-convex Integrals. J. Funct. Anal. 109 (1992) 76–97. | DOI | MR | Zbl
and ,Image Decomposition into a Bounded Variation Component and an Oscillating Component. J. Math. Imaging and Vision 22 (2005) 71–88. | DOI | MR | Zbl
, , and ,L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Clarendon Press, Oxford (2000). | MR | Zbl
Functionals with linear growth defined on vector valued BV functions. J. Math. Pures Appl., IX. Sér. 70 (1991) 269–323. | MR | Zbl
, and ,Dimensional reduction for energies with linear growth involving the bending moment. J. Math. Pures Appl. 90 (2008) 520–549. | DOI | MR | Zbl
, and ,Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. Annales de l’Institut Henri Poincaré (C) Analyse Non Linéaire 7 (1990) 67–90. | DOI | Numdam | MR | Zbl
,J. Ball and A. Zarnescu, Partial regularity and smooth topology-preserving approximations of rough domains, . | arXiv
Anisotropic singular perturbations-the vectorial case, Proc. Royal Soc. Edinb. A 124 (1994) 527–571. | MR | Zbl
and ,Bending moment in membrane theory. J. Elasticity 73 (2003) 75–99. | MR | Zbl
, and ,An homogenization result in . J. Convex Anal. 18 (2011) 1093–1126. | MR | Zbl
, and ,Thin elastic films: the impact of higher order perturbations.Quart. Appl. Math. 65 (2007) 69–98. | MR | Zbl
, and ,Relaxation in of functionals depending on strain and composition, Lions, edited by Jacques-Louis et al., Boundary value problems for partial differential equations and applications. Dedicated to Enrico Magenes on the occasion of his 70th birthday. Paris: Masson. Res. Notes Appl. Math. 29 (1993) 113–152. | MR | Zbl
, and ,Energy functionals depending on elastic strain and chemical composition. Calc. Var. Partial Differential Equations 2 (1994) 283–313. | MR | Zbl
, and ,I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: spaces. Springer Verlag (2007). | MR | Zbl
Quasiconvex integrands and Lower Semicontinuity in . Siam. J. Math. Anal. 23 (1992) 1081–1098. | MR | Zbl
and ,Relaxation of quasiconvex functionals in for integrands . Arch. Rational Mech. Anal. 123 (1993) 1–49. | DOI | MR | Zbl
and ,Relaxation of multiple integrals in the space . Proc. Roy. Soc. Edinburgh A 121 (1992) 321–348. | DOI | MR | Zbl
and ,Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results. Arch. Ration. Mech. Anal. 154 (2000) 101–134. | DOI | MR | Zbl
and ,Y. Meyer, Oscillating pattern in image processing and nonlinear evolution equations. The fifteenth Dean Jacqueline B. Lewis memorial lectures. Vol. 22 of University Lecture Series. Providence, RI. American Mathematical Society (AMS) (2001). | MR | Zbl
Relaxation of Certain Integral Functionals Depending on Strain and Chemical Composition. Chin. Ann. Math. 34B (2013) 491–514. | DOI | MR | Zbl
and ,Lower semicontinuous envelopes in . Banach Center Publications 101 (2014) 187–206. | DOI | MR | Zbl
and ,A.M. Ribeiro and E. Zappale, Erratum: Lower semicontinuous envelopes in 101 (2014), online.
Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259–268. | DOI | MR | Zbl
, and ,E.M. Stein, Singular integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970). | MR | Zbl
Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci. Comput. 19 (2003) 553–572. | DOI | MR | Zbl
and ,Image denoising and decomposition with total variation minimization and oscillatory functions. J. Math. Imaging Vision 20 (2004) 7–18. | DOI | MR | Zbl
and ,Cité par Sources :