A New $L^1$-Lower Semicontinuity Result

Graziani, Daniele. "A New $L^1$-Lower Semicontinuity Result." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 797-818. <http://eudml.org/doc/290417>.

@article{Graziani2007,
abstract = {The aim of this work is to prove a chain rule and an $L^1$-lower semicontinuity theorems for integral functional defined on $BV(\Omega)$. Moreover we apply this result in order to obtain new relaxation and $\Gamma$-convergence result without any coerciveness and any continuity assumption of the integrand $f(x, s, p)$ with respect to the variable $s$.},
author = {Graziani, Daniele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {797-818},
publisher = {Unione Matematica Italiana},
title = {A New $L^1$-Lower Semicontinuity Result},
url = {http://eudml.org/doc/290417},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Graziani, Daniele
TI - A New $L^1$-Lower Semicontinuity Result
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 797
EP - 818
AB - The aim of this work is to prove a chain rule and an $L^1$-lower semicontinuity theorems for integral functional defined on $BV(\Omega)$. Moreover we apply this result in order to obtain new relaxation and $\Gamma$-convergence result without any coerciveness and any continuity assumption of the integrand $f(x, s, p)$ with respect to the variable $s$.
LA - eng
UR - http://eudml.org/doc/290417
ER -

References

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AMAR, M. - DE CICCO, V., A continuity result for integral functionals defined on $BV(\Omega)$ , to appear. Zbl0735.49010
AMBROSIO, L., New lower semicontinuity result for integral functionals, Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 11, no. 1 (1987), 1-42. Zbl0642.49007 MR930856
AMBROSIO, L. - FUSCO, N. - PALLARA, D., Functions of bounded variation and free discontinuity problems, Oxford University Press (2000). Zbl0957.49001 MR1857292
BRAIDES, A., $\Gamma$ -convergence for beginners, Oxford University Press, New york (2000). MR1968440 DOI10.1093/acprof:oso/9780198507840.001.0001
BOUCHITTÉ, E. - FONSECA, I. MASCARENHAS, L., A global method for relaxation, Arch. Rat. Mech. Anal., 145, no. 1 (1998). MR1656477 DOI10.1007/s002050050124
DAL MASO, G., Integral representation on $BV(\Omega)$ of $\Gamma$ -limit of variational integrals, Manuscripta Math., 30 (1980), 387-416. Zbl0435.49016 MR567216 DOI10.1007/BF01301259
DAL MASO, G., Introduction to $\Gamma$ -convergence, Birkhauser, Boston (1993). Zbl0816.49001 MR1201152 DOI10.1007/978-1-4612-0327-8
DAL MASO, G. - LE FLOCH, P. G. - MURAT, F., Definition and weak stability of nonconservative product, J. Math. Pures Appl., 74 (1995), 483-548. Zbl0853.35068 MR1365258
DE CICCO, V., A lower semicontinuity result for functionals defined on $BV(\Omega)$ . Ricerche di Mat., 39 (1990), 293-325. Zbl0735.49010 MR1114522
DE CICCO, V., Lower semicontinuity result for certain functionals defined on $BV(\Omega)$ , Boll. U.M.I5-B (1991), 291-313. Zbl0738.46012 MR1111124
DE CICCO, V. - FUSCO, N. - VERDE, A., A chain rule formula in $BV(\Omega)$ and application to lower semicontinuity, to appear on Calc. Var. Zbl1136.49011 MR2293980 DOI10.1007/s00526-006-0048-7
DE CICCO, V. - FUSCO, N. - VERDE, A., On $L^{1}$ -lower semicontinuity on $BV(\Omega)$ . To appear on J. on Convex Analysis. MR2135805
DE CICCO, V. - LEONI, G., A chain rule in $L^{1}(\operatorname{div};\Omega)$ and its applications to lower semicontinuity, Calc. Var., 19 (2004), 23-51. Zbl1056.49019 MR2027846 DOI10.1007/s00526-003-0192-2
DE GIORGI, E., Teoremi di semicontinuità nel Calcolo Delle Variazioni, Istituto Nazionale di Alta Matematica, 1968-1969.
DE GIORGI, E. - BUTTAZZO, G. - DAL MASO, G., On the lower semicontinuity of certain integral functionals, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 74 (1983), 274-282. Zbl0554.49006 MR758347
DE GIORGI, E. - FRANZONI, T., Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Mat. Natur., 58 (1975), 842-850. MR448194
DE GIORGI, E. - FRANZONI, T., Su un tipo di convergenza variazionale, Rend. Sem. Mat. Brescia, 3 (1979), 63-101.
FONSECA, I. - LEONI, G., On lower semicontinuity and relaxation, Proc. R. Soc. Edim., Sect. A, Math., 131 (2001), 519-565. Zbl1003.49015 MR1838501 DOI10.1017/S0308210500000998
FUSCO, N. - GIANNETTI, F. - VERDE, A., A remark on the $L^{1}$ -lower semicontinuity for integral functionals in $BV(\Omega)$ , Manuscripta Math., 112 (2003), 313-323. Zbl1030.49014 MR2067041 DOI10.1007/s00229-003-0400-6
FUSCO, N. - GORI, M. - MAGGI, F., A remark on the Serrin's theorem, to appear. Zbl1215.49024 MR2314327 DOI10.1007/s00030-006-4018-8
GORI, M. - MARCELLINI, P., An extension of the Serrin's lower semicontinuity theorem, J. on Convex Analysis, 9 (2002). Zbl1019.49021 MR1970568
GORI, M. - MAGGI, F. - MARCELLINI, P., Some sharp condition for lower semicontinuity in $L^{1}$ , Diff. Int. Equations, 16 (2003), 51-76. Zbl1028.49012 MR1948872
MIRANDA, M., Superfici cartesiane generalizzate ed insiemi aperti di perimetro localmente finito sui prodotti cartesiani, Ann. Scuola Norm. Sup. Pisa, 18 (1964), 515-542. Zbl0152.24402 MR174706
SERRIN, J., On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc., 161 (1961), 139-167. Zbl0102.04601 MR138018 DOI10.2307/1993416

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