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Numerical methods for dividend optimization using regime-switching jump-diffusion models
Cesari-type conditions for semilinear elliptic equation with leading term containing controls
| 1. | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
| 2. | School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433 |
References:
| [1] |
G. Allaire, "Shape Optimization by the Homogenization Method," Springer, New York, 2002. |
| [2] |
A. Bensoussan, J. L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structures," North-Holland Company, Amsterdam, 1978. |
| [3] |
E. Cabib and G. Dal Maso, On a class of optimum problems in structural design, J. Optim. Theory Appl., 56 (1988), 39-65.
doi: 10.1007/BF00938526. |
| [4] |
L. Cesari, "Optimization Theory and Applications, Problems with Ordinary Equations," Applications of Mathematics 17, Springer, New York, 1983. |
| [5] |
A. F. Filippov, On certain questions in the theory of optimal control, SAIM J. Control Optim., 1 (1962), 76-84. |
| [6] |
X. Li and J. Yong, "Optimal Control Theory for Infinite Dimensional Systems," Birkhäuser, Boston, 1995. |
| [7] |
N. G. Meyers, An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Sc. Norm. Sup. Pisa, 17 (1963), 189-206. |
| [8] |
G. Milton and R. V. Kohn, Variational bounds on the effective moduli of anisotropic composites, J. Mech. Phys. Solids, 36 (1988), 597-629. |
| [9] |
F. Murat and L. Tartar, H-convergence, in: "Topics in the Mathematical Modelling of Composites Materials" (Eds. A. Cherkaev, R.V. Kohn), Boston, Birkhäuser, Boston 1997, 21-44 (French version: F. Murat, H-convergence, Mimeographed notes, Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger, 1978). |
| [10] |
F. Murat and L. Tartar, Calculus of variations and homogenization, in: "Topics in the Mathematical Modelling of Composites Materials" (Eds. A. Cherkaev, R. V. Kohn), Birkhäuser," Boston 1997, 139-173 (French version: F. Murat, Calcul des variations et homogénéisation, in: Les méthodes de l'homogénéisation, théorie et applications en physique, Coll. Dir. Etudes et Recherches EDF, Eyrolles, 1985, 319-369). |
| [11] |
L. Tartar, Estimations fines des coefficitents homogénéisés, Ennio de Giorgi colloquium, P. Krée ed., Pitman Research Notes in Math., 125 (1985), 168-187.
doi: i:10.1016/0022-5096(88)90001-4. |
| [12] |
J. Warga, "Optimal Control of Differential and Functional Equations," Academic Press, New York, 1972. |
show all references
References:
| [1] |
G. Allaire, "Shape Optimization by the Homogenization Method," Springer, New York, 2002. |
| [2] |
A. Bensoussan, J. L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structures," North-Holland Company, Amsterdam, 1978. |
| [3] |
E. Cabib and G. Dal Maso, On a class of optimum problems in structural design, J. Optim. Theory Appl., 56 (1988), 39-65.
doi: 10.1007/BF00938526. |
| [4] |
L. Cesari, "Optimization Theory and Applications, Problems with Ordinary Equations," Applications of Mathematics 17, Springer, New York, 1983. |
| [5] |
A. F. Filippov, On certain questions in the theory of optimal control, SAIM J. Control Optim., 1 (1962), 76-84. |
| [6] |
X. Li and J. Yong, "Optimal Control Theory for Infinite Dimensional Systems," Birkhäuser, Boston, 1995. |
| [7] |
N. G. Meyers, An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Sc. Norm. Sup. Pisa, 17 (1963), 189-206. |
| [8] |
G. Milton and R. V. Kohn, Variational bounds on the effective moduli of anisotropic composites, J. Mech. Phys. Solids, 36 (1988), 597-629. |
| [9] |
F. Murat and L. Tartar, H-convergence, in: "Topics in the Mathematical Modelling of Composites Materials" (Eds. A. Cherkaev, R.V. Kohn), Boston, Birkhäuser, Boston 1997, 21-44 (French version: F. Murat, H-convergence, Mimeographed notes, Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger, 1978). |
| [10] |
F. Murat and L. Tartar, Calculus of variations and homogenization, in: "Topics in the Mathematical Modelling of Composites Materials" (Eds. A. Cherkaev, R. V. Kohn), Birkhäuser," Boston 1997, 139-173 (French version: F. Murat, Calcul des variations et homogénéisation, in: Les méthodes de l'homogénéisation, théorie et applications en physique, Coll. Dir. Etudes et Recherches EDF, Eyrolles, 1985, 319-369). |
| [11] |
L. Tartar, Estimations fines des coefficitents homogénéisés, Ennio de Giorgi colloquium, P. Krée ed., Pitman Research Notes in Math., 125 (1985), 168-187.
doi: i:10.1016/0022-5096(88)90001-4. |
| [12] |
J. Warga, "Optimal Control of Differential and Functional Equations," Academic Press, New York, 1972. |
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