@article{AIHPC_2004__21_5_543_0, author = {Busca, J\'er\^ome and Sirakov, Boyan}, title = {Harnack type estimates for nonlinear elliptic systems and applications}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {543--590}, publisher = {Elsevier}, volume = {21}, number = {5}, year = {2004}, doi = {10.1016/j.anihpc.2003.06.001}, mrnumber = {2086750}, zbl = {02116180}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.001/} }
TY - JOUR AU - Busca, Jérôme AU - Sirakov, Boyan TI - Harnack type estimates for nonlinear elliptic systems and applications JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 543 EP - 590 VL - 21 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.001/ DO - 10.1016/j.anihpc.2003.06.001 LA - en ID - AIHPC_2004__21_5_543_0 ER -
%0 Journal Article %A Busca, Jérôme %A Sirakov, Boyan %T Harnack type estimates for nonlinear elliptic systems and applications %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 543-590 %V 21 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.001/ %R 10.1016/j.anihpc.2003.06.001 %G en %F AIHPC_2004__21_5_543_0
Busca, Jérôme; Sirakov, Boyan. Harnack type estimates for nonlinear elliptic systems and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 5, pp. 543-590. doi : 10.1016/j.anihpc.2003.06.001. http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.001/
[1] Harnack's inequality for cooperative weakly coupled elliptic systems, Comm. Partial Differential Equations 24 (9-10) (1999) 1555-1571. | MR | Zbl
, , ,[2] The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1) (1994) 47-92. | MR | Zbl
, , ,[3] Existence of the principal eigenfunction for cooperative elliptic systems in a general domain, Differential Equations (Differentsial'nye Uravneniya) 35 (3) (1999), (in Russian). | MR | Zbl
, , ,[4] A Markov modulated financial model, J. Comm. Statist.: Stoch. Models 14 (1998) 225-240. | MR | Zbl
,[5] M. Bladt, P. Padilla, Nonlinear financial models: finite Markov modulation and limits, Preprint.
[6] Existence results for Bellman equations and maximum principles in unbounded domains, Comm. Partial Differential Equations 24 (11-12) (1999) 2023-2042. | MR | Zbl
,[7] Interior estimates for fully nonlinear elliptic equations, Ann. of Math. 130 (1989) 189-213. | MR | Zbl
,[8] Fully Nonlinear Elliptic Equations, Amer. Math. Soc. Collog. Publ., vol. 43, American Mathematical Society, Providence, RI, 1995. | MR | Zbl
, ,[9] On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math 49 (1996) 365-397. | MR | Zbl
, , , ,[10] Harnack principle for weakly coupled elliptic systems, J. Differential Equations 39 (1997) 261-282. | MR | Zbl
, ,[11] Potential theory for elliptic systems, Ann. Probab. 24 (1) (1996) 293-319. | MR | Zbl
, ,[12] User's guide to viscosity solutions of second-order partial differential equations, Bull. Amer. Math. Soc. 27 (1) (1992) 1-67. | MR | Zbl
, , ,[13] Lp theory for fully nonlinear uniformly parabolic equations, Comm. Partial Differential Equations 25 (11&12) (2000) 1997-2053. | MR | Zbl
, , ,[14] Monotonicity and symmetry of solutions of elliptic systems in general domains, Nonlinear Differential Equations Appl. 1 (1994) 119-123. | MR | Zbl
,[15] Maximum principles for linear elliptic systems, Rend. Inst. Mat. Univ. Trieste (1992) 36-66. | MR | Zbl
, ,[16] Maximum principles for cooperative elliptic systems, C. R. Acad. Sci. Paris, Ser. I 310 (2) (1990) 49-52. | MR | Zbl
, ,[17] Un esempio di estremali discontinue per un problema variazionale di tipo elliptico, Boll. Un. Mat. Ital. 1 (4) (1968) 135-137. | MR | Zbl
,[18] Note on polyharmonic functions, Proc. Amer. Math. Soc. 12 (1961) 110-115. | MR | Zbl
, ,[19] On n-metaharmonic functions and harmonic functions of infinite order, Proc. Amer. Math. Soc. 8 (1957) 223-229. | MR | Zbl
,[20] Sur les valeurs moyennes des fonctions, Math. Ann. 119 (1944) 288-320. | MR | Zbl
,[21] Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. Math. Stud., vol. 105, Princeton University Press, 1983. | MR | Zbl
,[22] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1998. | Zbl
, ,[23] Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997) 589. | MR | Zbl
, ,[24] Classical solutions for some higher order semilinear elliptic equations under weak growth conditions, Nonlinear Anal. 28 (1997) 799-807. | MR | Zbl
, ,[25] On the eigenvalue problem for weakly coupled elliptic systems, Arch. Rational Mech. Anal. 81 (2) (1983) 151-159. | MR | Zbl
,[26] On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order, Ann. Sc. Norm. Sup. Pisa Cl. Sci. 4 (1) (1977) 145-178. | Numdam | MR | Zbl
, ,[27] Viscosity solutions for monotone systems of second-order elliptic PDE's, Comm. Partial Differential Equations 16 (6 & 7) (1991) 1095-1128. | MR | Zbl
, ,[28] The maximum principle for viscosity solutions of fully nonlinear seoncd order partial differential equations, Arch. Rational Mech. Anal. 101 (1988) 1-27. | MR | Zbl
,[29] A uniqueness result for viscosity solutions of fully nonlinear second order partial differential equations, Proc. Amer. Math. Soc. 4 (1988) 975-978. | MR | Zbl
, , ,[30] Nonlinear Elliptic and Parabolic Equations of Second Order, Coll. Math. Appl., 1987. | MR | Zbl
,[31] Large deviations for diffusion process coupled by a jump process, C. R. Acad. Sci. Paris, Sér. I 321 (1995) 849-854. | MR | Zbl
, ,[32] A system of nonlinear PDE's arising in the optimal control of stochastic systems, SIAM J. Appl. Math. 43 (1983) 465-475. | MR | Zbl
, ,[33] Diseguanza di Harnack per sistemi elliptici debolmente accopiati, Boll. Un. Mat. Ital. A 14 (5) (1977) 313-332. | MR | Zbl
,[34] Mathematical Biology, Springer-Verlag, 1993. | MR | Zbl
,[35] On the Harnack principle for strongly elliptic systems with nonsmooth coefficients, Comm. Pure Appl. Math. 52 (1999) 1213-1230. | MR | Zbl
,[36] Les fonctions polyharmoniques, Hermann & Cie, Paris, 1936. | Zbl
,[37] On multiply superharmonic functions, Uspekhi Math. Nauk 16 (3) (1961) 197-200, (in Russian). | MR | Zbl
,[38] Local behaviour of solutions of quasilinear equations, Acta Math. 111 (1964) 247-302. | MR | Zbl
,[39] Une propriété de moyenne des fonctions biharmoniques, Bull. Sci. Math. (2) 109 (1985) 103-111. | MR | Zbl
,[40] Strong positivity in C() for elliptic systems, Math. Z. 209 (1992) 251-271. | Zbl
,[41] On the regularity theory of fully nonlinear parabolic equations: I, Comm. Pure Appl. Math. 45 (1) (1992) 27-76. | MR | Zbl
,Cité par Sources :