Second-order elliptic integro-differential equations : viscosity solutions' theory revisited
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 3, page 567-585
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBarles, Guy, and Imbert, Cyril. "Second-order elliptic integro-differential equations : viscosity solutions' theory revisited." Annales de l'I.H.P. Analyse non linéaire 25.3 (2008): 567-585. <http://eudml.org/doc/78801>.
@article{Barles2008,
author = {Barles, Guy, Imbert, Cyril},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {viscosity solution; Jensen-Ishii lemma; comparison theorems; Lévy operators; stability; nonlinear elliptic integrodifferential equations; limiting semi-jets},
language = {eng},
number = {3},
pages = {567-585},
publisher = {Elsevier},
title = {Second-order elliptic integro-differential equations : viscosity solutions' theory revisited},
url = {http://eudml.org/doc/78801},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Barles, Guy
AU - Imbert, Cyril
TI - Second-order elliptic integro-differential equations : viscosity solutions' theory revisited
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 3
SP - 567
EP - 585
LA - eng
KW - viscosity solution; Jensen-Ishii lemma; comparison theorems; Lévy operators; stability; nonlinear elliptic integrodifferential equations; limiting semi-jets
UR - http://eudml.org/doc/78801
ER -
References
top- [1] N. Alibaud, C. Imbert, A non-local perturbation of first order Hamilton–Jacobi equations with unbounded data, submitted for publication, 2007.
- [2] Alvarez O., Tourin A., Viscosity solutions of nonlinear integro-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire13 (3) (1996) 293-317. Zbl0870.45002MR1395674
- [3] Arisawa M., A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations, Ann. Inst. H. Poincaré23 (5) (2006) 695-711. Zbl1105.45004MR2259613
- [4] Arisawa M., Corrigendum in the comparison theorems in “a new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations”, Ann. Inst. H. Poincaré24 (1) (2006) 167-169. Zbl1125.45008MR2286563
- [5] Barles G., Buckdahn R., Pardoux E., Backward stochastic differential equations and integral-partial differential equations, Stochastics Stochastics Rep.60 (1–2) (1997) 57-83. Zbl0878.60036MR1436432
- [6] Bensaoud I., Sayah A., Stability results for Hamilton–Jacobi equations with integro-differential terms and discontinuous Hamiltonians, Arch. Math. (Basel)79 (5) (2002) 392-395. Zbl1022.35004MR1951309
- [7] Bertoin J., Lévy processes, Cambridge Tracts in Mathematics, vol. 121, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
- [8] Crandall M.G., Ishii H., Lions P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.)27 (1) (1992) 1-67. Zbl0755.35015MR1118699
- [9] Garroni M.G., Menaldi J.L., Second Order Elliptic Integro-Differential Problems, Chapman & Hall/CRC Research Notes in Mathematics, vol. 430, Chapman & Hall/CRC, Boca Raton, FL, 2002. Zbl1014.45002MR1911531
- [10] Imbert C., A non-local regularization of first order Hamilton–Jacobi equations, J. Differential Equations211 (1) (2005) 218-246. Zbl1073.35059MR2121115
- [11] C. Imbert, R. Monneau, E. Rouy, Homogenization of first order equations with -periodic Hamiltonians. Part II: application to dislocation dynamics, Commun. Partial Differential Equations, submitted for publication. Zbl1143.35005MR2398239
- [12] Ishii H., On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm. Pure Appl. Math.42 (1) (1989) 15-45. Zbl0645.35025MR973743
- [13] Jakobsen E.R., Karlsen K.H., A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations, NoDEA Nonlinear Differential Equations Appl.13 (2) (2006) 137-165. Zbl1105.45006MR2243708
- [14] Jensen R., The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal.101 (1) (1988) 1-27. Zbl0708.35019MR920674
- [15] Øksendal B., Sulem A., Applied Stochastic Control of Jump Diffusions, Universitext, Springer-Verlag, Berlin, 2005. Zbl1074.93009MR2109687
- [16] Pham H., Optimal stopping of controlled jump diffusion processes: a viscosity solution approach, J. Math. Systems Estim. Control8 (1) (1998), 27 pp. (electronic). Zbl0899.60039MR1650147
- [17] Sayah A., Équations d'Hamilton–Jacobi du premier ordre avec termes intégro-différentiels. I. Unicité des solutions de viscosité. II. Existence de solutions de viscosité, Comm. Partial Differential Equations16 (6–7) (1991) 1057-1093. Zbl0742.45005MR1116853
- [18] Silvestre L., Hölder estimates for solutions of integro-differential equations like the fractional Laplace, Indiana Univ. Math. J.55 (3) (2006) 1155-1174. Zbl1101.45004MR2244602
- [19] Soner H.M., Optimal control with state-space constraint. II, SIAM J. Control Optim.24 (6) (1986) 1110-1122. Zbl0619.49013MR861089
- [20] Woyczyński W.A., Lévy processes in the physical sciences, in: Lévy processes, Birkhäuser Boston, Boston, MA, 2001, pp. 241-266. Zbl0982.60043MR1833700
Citations in EuDML Documents
top- Dan Goreac, Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
- Dan Goreac, Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
- Dan Goreac, Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.