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Primo Brandi

Department of Mathematics, University of Perugia, Via L. Vanvitelli, I-06123 Perugia, Italy.

Anna Salvadori

Department of Mathematics, University of Perugia, Via L. Vanvitelli, I-06123 Perugia, Italy.

References

  1. L.Ambrosio: New lower semicontinuity results for integral functionals, Rend. Accad. Naz. XL, 11 (1987), 1-42;Google Scholar
  2. E.Balder: (a) A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control and Opt., 22 (1984), 570-598; (b) On seminormality of integral functionals and their integrands, SIAM J. Control and Opt., 24 (1986), 95-121;https://doi.org/10.1137/0322035https://doi.org/10.1137/0324005Google Scholar
  3. P.Brandi, A.Salvadori: (a) Non-smooth solutions in plastic deformation, Atti Sem. Mat. Fis. Univ. Modena, 41 (1993), 483-490; (b) A variational approach to problems of plastic deformation, Developments in Partial Differential Equations and Applications to Mathematical Physics, G.Buttazzo, G.P.Galdi and L.Zanghirati Ed., Plenum Press (l992), 219-226; (c) A mean value property for lower semicontinuity on BV, Atti Sem. Mat. Fis. Univ. Modena 43 (1995); (d) Quasi convex integrands and lower semicontinuity in BV, to appear;https://doi.org/10.1007/978-1-4615-3032-9_16Google Scholar
  4. P.Brandi, A.Salvadori, W.H.Yang: Second order problems in plasticity with general distributional input, to appear;Google Scholar
  5. G.Buttazzo: Semicontinuity, relaxation, and integral representation in the calculus of variations, Pitman Research Notes in Math., 207 Longmans, Harlow, (1989);Google Scholar
  6. P.L.Butzer, R.J.Nessel: Fourier Analysis and Approximation, Birkhauser (1971);https://doi.org/10.1007/978-3-0348-7448-9Google Scholar
  7. C.Castaing, P.Clauzure: Semicontinuité des functionelles integrales, Séminaire d’Analyse Convexe, Université des Sciences et Techniques du Languedoc, Montpellier 11 (1981), exposé n. 15;Google Scholar
  8. C.Castaing, M.Valadier: Convex Analysis and Measurable Multifunctions, Lecture Notes 570 Springer-Verlag, (1977),;https://doi.org/10.1007/BFb0087685Google Scholar
  9. L.Cesari, (a) Sulle funzioni a variazione limitata, Ann. Scuola Nor. Sup. Pisa, 5 (1936), 299-313; (b) Seminormality and upper semicontinuity in optimal control, J.Opt. Theor. Appl., 6 (1970), 114-137; (c) Existence theorems for abstract multidimentional control problems, J. Opt. Theor. Appl. 6 (1970), 210-236; (d) Closure theorems for orientor fields and weak convergence, Arch. Rat. Mech. Anal., 55 (1974), 332-356; (e) Optimization Theory and Applications, Springer Verlag (1983); (f) Existence of discontinuous absolute minima for certain multiple integrals without growth properties, Rend. Accad. Naz. Lincei, 82 (1988), 661-671; (g) Existence of BV absolute discontinuous minima of modified multiple integrals of the calculus of variations, Rend. Circ. Mat. Palermo, 39 (1990), 169-209; (h) Rankine-Hugoniot type properties in terms of BV solutions of certain problems of the calculus of variations, Rend. Circ. Mat. Palermo, to appear;Google Scholar
  10. L.Cesari, T.S.Angell: On the Lavrentiev phenomenon, Calcolo, 22 (1985), 17-29;https://doi.org/10.1007/BF02576198Google Scholar
  11. L.Cesari, P.Brandi, A.Salvadori, (a) Discontinuous solutions in problems of optimization, Ann. Scuola Norm. Sup. Pisa, 15 (1988), 219-237; (b) Existence theorems concerning simple integrals of the calculus of variations for discontinuous solutions, Arch. Rat. Mech. Anal., 98 (1987), 307-328; (c) Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions, Ann. Mat. Pura Appl., 152 (1988), 95-121; (d) Seminormality conditions in calculus of variations for BV solutions, Ann. Mat. Pura Appl., 162 (1992), 299-317; (e) Existence theorems for multiple integrals with distributional constraints, Rapporto interno Dip. Matematica Univ. Perugia, 12 (1991);https://doi.org/10.1007/BF00276912https://doi.org/10.1007/BF01766143https://doi.org/10.1007/BF01760012Google Scholar
  12. L.Cesari, D.E.Cowles: Existence theorems in multidimentional problems of optimization with distributed and boundary controls, Arch. Rat. Mech. Anal., 46 (1972), 321-355;https://doi.org/10.1007/BF00281101Google Scholar
  13. L.Cesari, M.B.Suryanarayana, (a) Closure theorems without seminormality conditions, J. Opt. Theor. Appl., 15 (1975), 441-465; (b) Existence theorems for Pareto optimization in Banach spaces, Bull. Amer. Math. Soc., 82 (1975), 306-308; (c) Existence theorems for Pareto optimization. Multivalued and Banach space valued functionals, Trans. Amer. Math. Soc., 244 (1978), 37-65;https://doi.org/10.1007/BF00933207https://doi.org/10.1090/S0002-9904-1976-14033-5https://doi.org/10.1090/S0002-9947-1978-0506609-1Google Scholar
  14. L.Cesari, W.H.Yang, (a) Serrin’s integrals and second order problems of plasticity, Proc. Royal Soc. Edimburg, 117 (1991), 193-201; (b) BV functions and first order problems of plasticity, J. Opt. Theor. Appl., to appear;https://doi.org/10.1017/S0308210500024677Google Scholar
  15. B.Dacorogna: Direct Methods in the Calculus of Variations, Springer Verlag, (1989);https://doi.org/10.1007/978-3-642-51440-1Google Scholar
  16. E.De Giorgi: Teoremi di Semicontinuità nel Calcolo delle Variazioni,, INdAM, Roma (1968-69);Google Scholar
  17. E.De Giorgi, G.Buttazzo, G.Dal Maso: On the lower semicontinuity of certain integral functionals, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 74 (1983), 274-282;Google Scholar
  18. G.Fichera, (a) Semicontinuity of multiple integrals in ordinary form, Arch. Rat. Mech. Anal., 17 (1964), 339-352; (b) Semicontinuità ed esistenza del minimo per una classe di integrali multipli, Rev. Roum. Math. Pures Appl., 12 (1967), 1217-1220;https://doi.org/10.1007/BF00250470Google Scholar
  19. G.B.Folland: Real Analysis. Modern Techniques and their Applications, J.Wiley & Sons, (1984);Google Scholar
  20. T.H.Hildebrandt: Theory of Integration, Academic Press, (1963);Google Scholar
  21. K.Krickeberg: Distributionen, Functionen beschrankter Variation und Lebesguescher Inhalt nichterparameterischer Flachen, Ann. Mat. Pura App., 44 (1957), 105-133;https://doi.org/10.1007/BF02415194Google Scholar
  22. T.Radò: Length and Area, Amer. Math. Soc. Colloquium Publ., 30 (1984);Google Scholar
  23. E.Rothe: An existence theorem in the calculus of variations based on Sobolev’s imbedding theorems, Arch. Rat. Mech. Anal., 21 (1965), 151-162.https://doi.org/10.1007/BF00266572Google Scholar
  24. C.Sadowsky: Interpolation of Operators and Singular Integrals: an Introduction to Harmonic Analysis, M.Dekker, (1979);Google Scholar
  25. S.Saks: Theory of the Integral, Monografie Matematyczne, Hafner Publ. 7 (1937);Google Scholar
  26. J.Serrin: On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc., 101 (1961), 139-167;https://doi.org/10.1090/S0002-9947-1961-0138018-9Google Scholar
  27. A.W.Stoddart: Semicontinuity of integrals, Trans. Amer. Math. Soc., 122 (1966), 120-135;https://doi.org/10.1090/S0002-9947-1966-0190816-6Google Scholar
  28. L.H.Turner: The direct method in the calculus of variations, Perdue University Ph.D Thesis, (1957).Google Scholar

Suggested citation

P. Brandi, A. Salvadori. “On Lower Semicontinuity in BV Setting.” Journal of Convex Analysis 1 (1994), No. 2, 151–172. https://doi.org/10.68381/jca01012

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press.