Convergence and extensions of variational problems with non-coercive functionals

• Autorzy: Ioffe A.
• Języki publikacji: EN

Abstrakty

EN

The paper is a transcript of the lecture given at the European Symposium on Well-Posedness in Optimization in Warsaw. It contains a complete theory of variational problems with integrands not depending on x, including existence and relaxation theorems, a complete description of solutions and the connection between variational convergences of functionals and convergence of value functions and solutions of associated variational problems with the main emphasis on functionals that lack coercivity.

Słowa kluczowe

EN

duality; coercivity; Gamma-convergence; relaxation; vector measures

PL

dwoistość; gamma-zbieżność; koercyjność; miara wektorowa; relaksacja

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2002
• Tom: Vol. 31, no. 3
• Strony: 507--519
• Opis fizyczny: Bibliogr. 9 poz.,

Twórcy

autor

Ioffe A.

• Department of Mathematics, Technion, Haifa 32000, Israel

Bibliografia

• ATTOUCH, H. (1984) Variational convergence for functions and operators. Appl. Math. Ser. , Pitman, Boston.
• BOUCHITTE, G. (1987) Representation integrale de fonctionnelles convexes sur un espace de mesures. II. Cas de l'epi-convergence. Ann.. Univ. Ferrara Sez. VII(N.S.) 33, 113- 156.
• BUTTAZZO, G. (1989) Semicontinuity, relaxition and integral representation in the calculus of variations. Pitman Res. Notes Math. Ser., vol. 207, Longman, Harlow.
• DALMASO, G. (1993) An introduction to Γ-convergence. Birkhauser, Boston.
• IOFFE A.D. and FREDDI, L. (2002) On limits of variational problems. The case of noll-coercive functionals, J. Convex Analysis (to appear).
• lOFFE, A.D. and TIHOMIROV, V.M. (1969) On minimalization of integral functionals. Funkt. Anal. iPrilozen. 3, 61-70 (in Russian; English transl.: Funct. Anal. Appl. 3 (1969), 218- 227).
• IOFFE, A.D. and TIHOMIROV, V.M. (1974) Theory of extremal problems.Nauka, Moscow (in Russian; English transl.: North-Holland Publishing Co., Amsterdarn-New York, 1979).
• ROCKAFELLAR, R.T. and WETS, R.J .B. (1997) Variational Analysis. Springer Verlag, Berlin- Heidelberg-New York.
• VALADIER, M. (1987) Functions and operators on the space of bounded measures. Atti Sem. Mat. Fis. Univ. Modena. (1985/86), 353- 361.