Harnack type estimates for nonlinear elliptic systems and applications

Jérôme Busca; Boyan Sirakov

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 5, page 543-590
  • ISSN: 0294-1449

How to cite

top

Busca, Jérôme, and Sirakov, Boyan. "Harnack type estimates for nonlinear elliptic systems and applications." Annales de l'I.H.P. Analyse non linéaire 21.5 (2004): 543-590. <http://eudml.org/doc/78630>.

@article{Busca2004,
author = {Busca, Jérôme, Sirakov, Boyan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {5},
pages = {543-590},
publisher = {Elsevier},
title = {Harnack type estimates for nonlinear elliptic systems and applications},
url = {http://eudml.org/doc/78630},
volume = {21},
year = {2004},
}

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
PB - Elsevier
VL - 21
IS - 5
SP - 543
EP - 590
LA - eng
UR - http://eudml.org/doc/78630
ER -

References

top
  1. [1] Arapostathis A., Ghosh M., Marcus St., Harnack's inequality for cooperative weakly coupled elliptic systems, Comm. Partial Differential Equations24 (9–10) (1999) 1555-1571. Zbl0934.35039MR1708101
  2. [2] Berestycki H., Nirenberg L., Varadhan S.R.S., The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math.47 (1) (1994) 47-92. Zbl0806.35129MR1258192
  3. [3] Birindelli I., Mitidieri E., Sweers G., Existence of the principal eigenfunction for cooperative elliptic systems in a general domain, Differential Equations (Differentsial'nye Uravneniya)35 (3) (1999), (in Russian). Zbl0940.35147MR1726799
  4. [4] Bladt M., A Markov modulated financial model, J. Comm. Statist.: Stoch. Models14 (1998) 225-240. Zbl0934.60061MR1617564
  5. [5] M. Bladt, P. Padilla, Nonlinear financial models: finite Markov modulation and limits, Preprint. 
  6. [6] Busca J., Existence results for Bellman equations and maximum principles in unbounded domains, Comm. Partial Differential Equations24 (11–12) (1999) 2023-2042. Zbl0961.35021MR1720774
  7. [7] Caffarelli L.A., Interior estimates for fully nonlinear elliptic equations, Ann. of Math.130 (1989) 189-213. Zbl0692.35017MR1005611
  8. [8] Caffarelli L.A., Cabre X., Fully Nonlinear Elliptic Equations, Amer. Math. Soc. Collog. Publ., vol. 43, American Mathematical Society, Providence, RI, 1995. Zbl0834.35002MR1351007
  9. [9] Caffarelli L.A., Crandall M.G., Kocan M., Świech A., On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math49 (1996) 365-397. Zbl0854.35032MR1376656
  10. [10] Chen Z.Q., Zhao Z., Harnack principle for weakly coupled elliptic systems, J. Differential Equations39 (1997) 261-282. Zbl0882.35039MR1472349
  11. [11] Chen Z.Q., Zhao Z., Potential theory for elliptic systems, Ann. Probab.24 (1) (1996) 293-319. Zbl0854.60062MR1387637
  12. [12] Crandall M.G., Ishii H., Lions P.-L., User's guide to viscosity solutions of second-order partial differential equations, Bull. Amer. Math. Soc.27 (1) (1992) 1-67. Zbl0755.35015MR1118699
  13. [13] Crandall M.G., Kocan M., Świech A., Lp theory for fully nonlinear uniformly parabolic equations, Comm. Partial Differential Equations25 (11&12) (2000) 1997-2053. Zbl0973.35097MR1789919
  14. [14] de Figueiredo D.G., Monotonicity and symmetry of solutions of elliptic systems in general domains, Nonlinear Differential Equations Appl.1 (1994) 119-123. Zbl0822.35039MR1273345
  15. [15] de Figueiredo D.G., Mitidieri E., Maximum principles for linear elliptic systems, Rend. Inst. Mat. Univ. Trieste (1992) 36-66. Zbl0793.35011MR1210477
  16. [16] de Figueiredo D.G., Mitidieri E., Maximum principles for cooperative elliptic systems, C. R. Acad. Sci. Paris, Ser. I310 (2) (1990) 49-52. Zbl0712.35021MR1044413
  17. [17] de Giorgi E., Un esempio di estremali discontinue per un problema variazionale di tipo elliptico, Boll. Un. Mat. Ital.1 (4) (1968) 135-137. Zbl0155.17603MR227827
  18. [18] Duffin R.J., Nehari Z., Note on polyharmonic functions, Proc. Amer. Math. Soc.12 (1961) 110-115. Zbl0097.08504MR141793
  19. [19] Friedman A., On n-metaharmonic functions and harmonic functions of infinite order, Proc. Amer. Math. Soc.8 (1957) 223-229. Zbl0077.30304MR85430
  20. [20] Ghermanescu M., Sur les valeurs moyennes des fonctions, Math. Ann.119 (1944) 288-320. Zbl0063.01603MR11489
  21. [21] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. Math. Stud., vol. 105, Princeton University Press, 1983. Zbl0516.49003MR717034
  22. [22] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1998. Zbl0562.35001
  23. [23] Grunau H., Sweers G., Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann.307 (1997) 589. Zbl0892.35031MR1464133
  24. [24] Grunau H., Sweers G., Classical solutions for some higher order semilinear elliptic equations under weak growth conditions, Nonlinear Anal.28 (1997) 799-807. Zbl0867.35031MR1422185
  25. [25] Hess P., On the eigenvalue problem for weakly coupled elliptic systems, Arch. Rational Mech. Anal.81 (2) (1983) 151-159. Zbl0509.35029MR682266
  26. [26] Hildebrandt S., Widman K.-O., 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. Zbl0353.35013MR457936
  27. [27] Ishii H., Koike S., Viscosity solutions for monotone systems of second-order elliptic PDE's, Comm. Partial Differential Equations16 (6 & 7) (1991) 1095-1128. Zbl0742.35022MR1116855
  28. [28] Jensen R., The maximum principle for viscosity solutions of fully nonlinear seoncd order partial differential equations, Arch. Rational Mech. Anal.101 (1988) 1-27. Zbl0708.35019MR920674
  29. [29] Jensen R., Lions P.L., Souganidis P.E., A uniqueness result for viscosity solutions of fully nonlinear second order partial differential equations, Proc. Amer. Math. Soc.4 (1988) 975-978. Zbl0662.35048MR934877
  30. [30] Krylov, Nonlinear Elliptic and Parabolic Equations of Second Order, Coll. Math. Appl., 1987. Zbl0619.35004MR934313
  31. [31] Lasry J.-M., Lions P.-L., Large deviations for diffusion process coupled by a jump process, C. R. Acad. Sci. Paris, Sér. I321 (1995) 849-854. Zbl0837.60026MR1355840
  32. [32] Lenhart S.M., Belbas S.A., A system of nonlinear PDE's arising in the optimal control of stochastic systems, SIAM J. Appl. Math.43 (1983) 465-475. Zbl0511.93077MR700525
  33. [33] Mandras, Diseguanza di Harnack per sistemi elliptici debolmente accopiati, Boll. Un. Mat. Ital. A14 (5) (1977) 313-332. Zbl0357.35003MR499700
  34. [34] Murray J.D., Mathematical Biology, Springer-Verlag, 1993. Zbl0682.92001MR1239892
  35. [35] Muscalu C., On the Harnack principle for strongly elliptic systems with nonsmooth coefficients, Comm. Pure Appl. Math.52 (1999) 1213-1230. Zbl0949.35046MR1699966
  36. [36] Nicolescu M., Les fonctions polyharmoniques, Hermann & Cie, Paris, 1936. Zbl0015.15905
  37. [37] Ovčarenko I.E., On multiply superharmonic functions, Uspekhi Math. Nauk16 (3) (1961) 197-200, (in Russian). Zbl0128.09901MR130389
  38. [38] Serrin J., Local behaviour of solutions of quasilinear equations, Acta Math.111 (1964) 247-302. Zbl0128.09101MR170096
  39. [39] Smyrnelis E.P., Une propriété de moyenne des fonctions biharmoniques, Bull. Sci. Math. (2)109 (1985) 103-111. Zbl0566.31004MR802527
  40. [40] Sweers G., Strong positivity in C( Ω ¯ ) for elliptic systems, Math. Z.209 (1992) 251-271. Zbl0727.35045
  41. [41] Wang L., On the regularity theory of fully nonlinear parabolic equations: I, Comm. Pure Appl. Math.45 (1) (1992) 27-76. Zbl0832.35025MR1135923

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.