메뉴 건너뛰기




Volumn 37, Issue 1, 2009, Pages 29-62

Relaxation of signed integral functionals in BV

Author keywords

[No Author keywords available]

Indexed keywords


EID: 70450239818     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-009-0250-5     Document Type: Article
Times cited : (84)

References (41)
  • 1
    • 34250138457 scopus 로고
    • Semicontinuity problems in the calculus of variations
    • Acerbi E., Fusco N.: Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal. 86, 125-145 (1984).
    • (1984) Arch. Rational Mech. Anal. , vol.86 , pp. 125-145
    • Acerbi, E.1    Fusco, N.2
  • 2
    • 84971972568 scopus 로고
    • Rank one property for derivatives of functions with bounded variation
    • Alberti G.: Rank one property for derivatives of functions with bounded variation. Proc. Roy. Soc. Edinburgh Sect. A 123, 239-274 (1993).
    • (1993) Proc. Roy. Soc. Edinburgh Sect. A , vol.123 , pp. 239-274
    • Alberti, G.1
  • 3
    • 21744438986 scopus 로고    scopus 로고
    • Non-uniform integrability and generalized Young measures
    • Alibert J. J., Bouchitté G.: Non-uniform integrability and generalized Young measures. J. Convex Anal. 4, 129-147 (1997).
    • (1997) J. Convex Anal. , vol.4 , pp. 129-147
    • Alibert, J.J.1    Bouchitté, G.2
  • 4
    • 34547513464 scopus 로고    scopus 로고
    • A relaxation result in BV for integral functionals with discontinuous integrands
    • Amar M., De Cicco V., Fusco N.: A relaxation result in BV for integral functionals with discontinuous integrands. ESAIM Control Optim. Calc. Var. 13, 396-412 (2007).
    • (2007) ESAIM Control Optim. Calc. Var. , vol.13 , pp. 396-412
    • Amar, M.1    de Cicco, V.2    Fusco, N.3
  • 5
    • 46749116522 scopus 로고    scopus 로고
    • Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands
    • Amar M., De Cicco V., Fusco N.: Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands. ESAIM Control Optim. Calc. Var. 14, 456-477 (2008).
    • (2008) ESAIM Control Optim. Calc. Var. , vol.14 , pp. 456-477
    • Amar, M.1    de Cicco, V.2    Fusco, N.3
  • 6
    • 38249008242 scopus 로고
    • On the relaxation in BV(Ω; Rm) of quasi-convex integrals
    • m) of quasi-convex integrals. J. Funct. Anal. 109, 76-97 (1992).
    • (1992) J. Funct. Anal. , vol.109 , pp. 76-97
    • Ambrosio, L.1    dal Maso, G.2
  • 7
    • 0003282839 scopus 로고    scopus 로고
    • Functions of Bounded Variation and Free-Discontinuity Problems
    • Oxford University Press, Oxford
    • Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free-Discontinuity Problems. Oxford Mathematical Monographs. Oxford University Press, Oxford (2000).
    • (2000) Oxford Mathematical Monographs
    • Ambrosio, L.1    Fusco, N.2    Pallara, D.3
  • 10
    • 0041090551 scopus 로고    scopus 로고
    • The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent
    • Bouchitté G., Fonseca I., Malý J.: The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent. Proc. Roy. Soc. Edinburgh Sect. A 128(3), 463-479 (1998).
    • (1998) Proc. Roy. Soc. Edinburgh Sect. A , vol.128 , Issue.3 , pp. 463-479
    • Bouchitté, G.1    Fonseca, I.2    Malý, J.3
  • 12
    • 85067946483 scopus 로고    scopus 로고
    • Direct methods in the calculus of variations
    • 2nd edn., Springer, New York
    • Dacorogna, B.: Direct methods in the calculus of variations, 2nd edn. Applied Mathematical Sciences, vol. 78, Springer, New York (2008).
    • (2008) Applied Mathematical Sciences , vol.78
    • Dacorogna, B.1
  • 13
    • 0002915127 scopus 로고
    • Integral functionals determined by their minima
    • Dal Maso G., Modica L.: Integral functionals determined by their minima. Rend. Sem. Mat. Univ. Padova 76, 255-267 (1986).
    • (1986) Rend. Sem. Mat. Univ. Padova , vol.76 , pp. 255-267
    • dal Maso, G.1    Modica, L.2
  • 15
    • 84974265500 scopus 로고
    • Lower semicontinuity and continuity of functions of measures with respect to the strict convergence
    • Delladio S.: Lower semicontinuity and continuity of functions of measures with respect to the strict convergence. Proc. Roy. Soc. Edinburgh Sect. A 119, 265-278 (1991).
    • (1991) Proc. Roy. Soc. Edinburgh Sect. A , vol.119 , pp. 265-278
    • Delladio, S.1
  • 16
    • 0003346795 scopus 로고
    • Measure theory and fine properties of functions
    • CRC Press, Boca Raton
    • Evans, L. C., Gariepy, R. F.: Measure theory and fine properties of functions. In: Studies in Advanced Mathematics, CRC Press, Boca Raton (1992).
    • (1992) Studies in Advanced Mathematics
    • Evans, L.C.1    Gariepy, R.F.2
  • 17
    • 84974173146 scopus 로고
    • Lower semicontinuity of surface energies
    • Fonseca I.: Lower semicontinuity of surface energies. Proc. Roy. Soc. Edinburgh Sect. A 120, 99-115 (1992).
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.120 , pp. 99-115
    • Fonseca, I.1
  • 21
    • 0001238431 scopus 로고
    • Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili
    • Gagliardo E.: Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili. Rend. Sem. Mat. Univ. Padova 27, 284-305 (1957).
    • (1957) Rend. Sem. Mat. Univ. Padova , vol.27 , pp. 284-305
    • Gagliardo, E.1
  • 22
    • 84972542010 scopus 로고
    • Sublinear functions of measures and variational integrals
    • Goffman C., Serrin J.: Sublinear functions of measures and variational integrals. Duke Math. J. 31, 159-178 (1964).
    • (1964) Duke Math. J. , vol.31 , pp. 159-178
    • Goffman, C.1    Serrin, J.2
  • 23
  • 24
    • 0001139965 scopus 로고
    • Characterizations of Young measures generated by gradients
    • Kinderlehrer D., Pedregal P.: Characterizations of Young measures generated by gradients. Arch. Rational Mech. Anal. 115(4), 329-365 (1991).
    • (1991) Arch. Rational Mech. Anal. , vol.115 , Issue.4 , pp. 329-365
    • Kinderlehrer, D.1    Pedregal, P.2
  • 25
    • 0033432488 scopus 로고    scopus 로고
    • Lower semicontinuity in spaces of weakly differentiable functions
    • Kristensen J.: Lower semicontinuity in spaces of weakly differentiable functions. Math. Ann. 313, 653-710 (1999).
    • (1999) Math. Ann. , vol.313 , pp. 653-710
    • Kristensen, J.1
  • 27
    • 0040739800 scopus 로고    scopus 로고
    • Lower semicontinuity of quasi-convex integrals in BV
    • Kristensen J.: Lower semicontinuity of quasi-convex integrals in BV. Calc. Var. Partial Differ. Equ. 7(3), 249-261 (1998).
    • (1998) Calc. Var. Partial Differ. Equ. , vol.7 , Issue.3 , pp. 249-261
    • Kristensen, J.1
  • 28
    • 0032363352 scopus 로고    scopus 로고
    • 1,1 and optimal jump microstructure in BV relaxation
    • (electronic)
    • 1,1 and optimal jump microstructure in BV relaxation. SIAM J. Math. Anal. 29, 823-848 (1998) (electronic).
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 823-848
    • Larsen, C.J.1
  • 29
    • 0002683104 scopus 로고
    • Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals
    • Marcellini P.: Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals. Manuscripta Math. 51, 1-28 (1985).
    • (1985) Manuscripta Math. , vol.51 , pp. 1-28
    • Marcellini, P.1
  • 30
    • 84968503702 scopus 로고
    • Quasi-convexity and lower semi-continuity of multiple variational integrals of any order
    • Meyers N. G.: Quasi-convexity and lower semi-continuity of multiple variational integrals of any order. Trans. Amer. Math. Soc. 119, 125-149 (1965).
    • (1965) Trans. Amer. Math. Soc. , vol.119 , pp. 125-149
    • Meyers, N.G.1
  • 31
    • 84972497511 scopus 로고
    • Quasiconvexity and the semicontinuity of multiple integrals
    • Morrey C. B. Jr: Quasiconvexity and the semicontinuity of multiple integrals. Pacific J. Math. 2, 25-53 (1952).
    • (1952) Pacific J. Math. , vol.2 , pp. 25-53
    • Morrey Jr., C.B.1
  • 34
    • 0002980282 scopus 로고
    • On quasiconvex functions which are homogeneous of degree 1
    • Müller S.: On quasiconvex functions which are homogeneous of degree 1. Indiana Univ. Math. J. 41, 295-301 (1992).
    • (1992) Indiana Univ. Math. J. , vol.41 , pp. 295-301
    • Müller, S.1
  • 36
    • 0001503348 scopus 로고
    • Weak convergence of completely additive vector functions on a set
    • Reshetnyak Y. G.: Weak convergence of completely additive vector functions on a set. Siberian Math. J. 9, 1039-1045 (1968).
    • (1968) Siberian Math. J. , vol.9 , pp. 1039-1045
    • Reshetnyak, Y.G.1
  • 39
    • 0037801570 scopus 로고
    • Quasiconvex functions with subquadratic growth
    • Šverák V.: Quasiconvex functions with subquadratic growth. Proc. Roy. Soc. London Ser. A 433, 723-725 (1991).
    • (1991) Proc. Roy. Soc. London Ser. A , vol.433 , pp. 723-725
    • Šverák, V.1
  • 40
    • 0001485671 scopus 로고
    • A construction of quasiconvex functions with linear growth at infinity
    • Zhang K.: A construction of quasiconvex functions with linear growth at infinity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 19, 313-326 (1992).
    • (1992) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.19 , Issue.4 , pp. 313-326
    • Zhang, K.1
  • 41
    • 0003320023 scopus 로고
    • Weakly differentiable functions
    • Springer
    • Ziemer, W. P.: Weakly differentiable functions. In: Graduate Texts in Mathematics, vol. 120. Springer, New York (1989).
    • (1989) Graduate Texts in Mathematics , vol.120
    • Ziemer, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.