December  2011, 31(4): 1017-1021. doi: 10.3934/dcds.2011.31.1017

Ennio De Giorgi and $\mathbf\Gamma$-convergence

1. 

SISSA, via Bonomea 265, 34136 Trieste, Italy

Received  March 2009 Revised  December 2010 Published  September 2011

$\Gamma$-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.
Citation: Gianni Dal Maso. Ennio De Giorgi and $\mathbf\Gamma$-convergence. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1017-1021. doi: 10.3934/dcds.2011.31.1017
References:
[1]

G. Alberti, L. Ambrosio and X. Cabré, On a long-standing conjecture of E. De Giorgi: Symmetry in 3D for general nonlinearities and a local minimality property,, Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday, 65 (2001), 9. doi: 10.1023/A:1010602715526. Google Scholar

[2]

G. Dal Maso and L. Modica, Nonlinear stochastic homogenization,, Ann. Mat. Pura Appl. (4), 144 (1986), 347. Google Scholar

[3]

G. Dal Maso and L. Modica, Nonlinear stochastic homogenization and ergodic theory,, J. Reine Angew. Math., 368 (1986), 28. Google Scholar

[4]

E. De Giorgi, Sulla convergenza di alcune successioni d'integrali del tipo dell'area,, Collection of articles dedicated to Mauro Picone on the occasion of his ninetieth birthday, 8 (1975), 277. Google Scholar

[5]

E. De Giorgi, $\Gamma$-convergenza e $G$-convergenza, Boll. Un., Mat. Ital. A (5), 14 (1977), 213. Google Scholar

[6]

E. De Giorgi, Convergence problems for functionals and operators,, in, (1979), 131. Google Scholar

[7]

E. De Giorgi, $\Gamma$-limiti di ostacoli,, in, (1981), 51. Google Scholar

[8]

E. De Giorgi, Generalized limits in calculus of variations,, in, (1981), 1980. Google Scholar

[9]

E. De Giorgi, Operatori elementari di limite ed applicazioni al Calcolo delle Variazioni,, Atti del convegno, (1982), 101. Google Scholar

[10]

E. De Giorgi, $G$-operators and $\Gamma$-convergence,, in, (1984), 1175. Google Scholar

[11]

E. De Giorgi and G. Buttazzo, Limiti generalizzati e loro applicazioni alle equazioni differenziali,, (Italian) [Generalized limits and their applications to differential equations], 36 (1981), 53. Google Scholar

[12]

E. De Giorgi and G. Dal Maso, $\Gamma$-convergence and the calculus of variations,, in, 979 (1983), 121. Google Scholar

[13]

E. De Giorgi, G. Dal Maso and P. Longo, $\Gamma$-limiti di ostacoli,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8), 68 (1980), 481. Google Scholar

[14]

E. De Giorgi, G. Dal Maso and L. Modica, Convergenza debole di misure su spazi di funzioni semicontinue,, Atti Accad. Naz. Lincei, 79 (1985), 98. Google Scholar

[15]

E. De Giorgi, G. Dal Maso and L. Modica, Weak convergence of measures on spaces of semicontinuous functions,, Proc. of the Int. Workshop on Integral Functionals in the Calculus of Variations (Trieste, 15 (1987), 59. Google Scholar

[16]

E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 58 (1975), 842. Google Scholar

[17]

E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale,, Rend. Sem. Mat. Brescia, 3 (1979), 63. Google Scholar

[18]

E. De Giorgi and T. Franzoni, Una presentazione sintetica dei limiti generalizzati,, (Italian) [Generalized limits: A synthesis), 41 (1982), 405. Google Scholar

[19]

E. De Giorgi and L. Modica, $\Gamma$-convergenza e superfici minime,, preprint Scuola Normale Superiore di Pisa, (1979). Google Scholar

[20]

E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine,, Boll. Un. Mat. Ital. (4), 8 (1973), 391. Google Scholar

[21]

O. Savin, Symmetry of entire solutions for a class of semilinear elliptic equations,, in, (2006), 257. Google Scholar

[22]

S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore,, Ann. Scuola Norm. Sup. Pisa (3), 21 (1967), 657. Google Scholar

[23]

S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche,, Ann. Scuola Norm. Sup. Pisa (3), 22 (1968), 571. Google Scholar

show all references

References:
[1]

G. Alberti, L. Ambrosio and X. Cabré, On a long-standing conjecture of E. De Giorgi: Symmetry in 3D for general nonlinearities and a local minimality property,, Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday, 65 (2001), 9. doi: 10.1023/A:1010602715526. Google Scholar

[2]

G. Dal Maso and L. Modica, Nonlinear stochastic homogenization,, Ann. Mat. Pura Appl. (4), 144 (1986), 347. Google Scholar

[3]

G. Dal Maso and L. Modica, Nonlinear stochastic homogenization and ergodic theory,, J. Reine Angew. Math., 368 (1986), 28. Google Scholar

[4]

E. De Giorgi, Sulla convergenza di alcune successioni d'integrali del tipo dell'area,, Collection of articles dedicated to Mauro Picone on the occasion of his ninetieth birthday, 8 (1975), 277. Google Scholar

[5]

E. De Giorgi, $\Gamma$-convergenza e $G$-convergenza, Boll. Un., Mat. Ital. A (5), 14 (1977), 213. Google Scholar

[6]

E. De Giorgi, Convergence problems for functionals and operators,, in, (1979), 131. Google Scholar

[7]

E. De Giorgi, $\Gamma$-limiti di ostacoli,, in, (1981), 51. Google Scholar

[8]

E. De Giorgi, Generalized limits in calculus of variations,, in, (1981), 1980. Google Scholar

[9]

E. De Giorgi, Operatori elementari di limite ed applicazioni al Calcolo delle Variazioni,, Atti del convegno, (1982), 101. Google Scholar

[10]

E. De Giorgi, $G$-operators and $\Gamma$-convergence,, in, (1984), 1175. Google Scholar

[11]

E. De Giorgi and G. Buttazzo, Limiti generalizzati e loro applicazioni alle equazioni differenziali,, (Italian) [Generalized limits and their applications to differential equations], 36 (1981), 53. Google Scholar

[12]

E. De Giorgi and G. Dal Maso, $\Gamma$-convergence and the calculus of variations,, in, 979 (1983), 121. Google Scholar

[13]

E. De Giorgi, G. Dal Maso and P. Longo, $\Gamma$-limiti di ostacoli,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8), 68 (1980), 481. Google Scholar

[14]

E. De Giorgi, G. Dal Maso and L. Modica, Convergenza debole di misure su spazi di funzioni semicontinue,, Atti Accad. Naz. Lincei, 79 (1985), 98. Google Scholar

[15]

E. De Giorgi, G. Dal Maso and L. Modica, Weak convergence of measures on spaces of semicontinuous functions,, Proc. of the Int. Workshop on Integral Functionals in the Calculus of Variations (Trieste, 15 (1987), 59. Google Scholar

[16]

E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 58 (1975), 842. Google Scholar

[17]

E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale,, Rend. Sem. Mat. Brescia, 3 (1979), 63. Google Scholar

[18]

E. De Giorgi and T. Franzoni, Una presentazione sintetica dei limiti generalizzati,, (Italian) [Generalized limits: A synthesis), 41 (1982), 405. Google Scholar

[19]

E. De Giorgi and L. Modica, $\Gamma$-convergenza e superfici minime,, preprint Scuola Normale Superiore di Pisa, (1979). Google Scholar

[20]

E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine,, Boll. Un. Mat. Ital. (4), 8 (1973), 391. Google Scholar

[21]

O. Savin, Symmetry of entire solutions for a class of semilinear elliptic equations,, in, (2006), 257. Google Scholar

[22]

S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore,, Ann. Scuola Norm. Sup. Pisa (3), 21 (1967), 657. Google Scholar

[23]

S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche,, Ann. Scuola Norm. Sup. Pisa (3), 22 (1968), 571. Google Scholar

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