Removable singularities for fully nonlinear elliptic equations

Archive for Rational Mechanics and Analysis

Volumn 155, Issue 3, 2000, Pages 201-214

  Labutin, Denis A ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034550789     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050000108     Document Type: Article

References (39)

1. AVILES, P., A study of the singularities of solutions of a class of nonlinear elliptic partial differential equations, Comm. Partial Differential Equations 1 (1982), 609-643.
2. BERS, L., Isolated singularities of minimal surfaces, Ann. of Math. 53 (1951), 364-386.
3. BREZIS, H. & NIRENBERG, L., Removable singularities for nonlinear elliptic equations, Topol. Methods Nonlinear Anal. 9 (1997), 201-219.
4. BREZIS, H. & VERON, L., Removable singularities for some nonlinear elliptic equations, Arch. Rational Mech. Anal. 75 (1980/81), 1-6.
5. CABRE, X. & CAFFARELLI, L. A., Fully nonlinear elliptic equations, Providence, RI, 1995.
6. CRANDALL, M. G., Viscosity solutions: a primer, 1-43, Lecture Notes in Math., 1660, Springer, Berlin, 1997.
7. CRANDALL, M. G., EVANS, L. C. & LIONS, P.-L., Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984), 487-502.
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 (1992), 1-67.
9. CRANDALL, M. G. & LIONS, P.-L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42.
10. DEGIORGI, E. & STAMPACCHIA, G., Sulle singolarita eliminabili delle ipersuperficie minimali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 38 (1965), 352-357.
11. DYNKIN, E. B., A probabilistic approach to one class of nonlinear differential equations, Probab. Theory Related Fields 89 (1991), 89-115.
12. DYNKIN, E. B. & KUZNETSOV, S. E., Superdiffusions and removable singularities for quasilinear partial differential equations, Comm. Pure Appl. Math. 49 (1996), 125-176.
13. DYNKIN, E. B. & KUZNETSOV, S. E., Trace on the boundary for solutions of nonlinear differential equations, Trans. Amer. Math. Soc. 350 (1998), 4499-4519.
14. DYNKIN, E. B. & KUZNETSOV, S. E., Fine topology and fine trace on the boundary associated with a class of semilinear differential equations, Comm. Pure Appl. Math. 51 (1998), 897-936.
15. DYNKIN, E. B. & KUZNETSOV, S. E., Extinction of superdiffusions and semilinear partial differential equations, J. Funct. Anal. 162 (1999), 346-378.
16. GILBARG, D. & TRUDINGER, N. S., Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1983.
17. ISHII, H., On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic partial-differential-equations, Comm. Pure Appi Math. 42 (1989), 15-45.
18. JENSEN, R., The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal. 101 (1988), 1-27.
19. JENSEN, R. R., Viscosity solutions of elliptic partial differential equations, Doc. Math., Extra Vol. III (1998), 31-38.
20. KONDRATJEV, V. A. & LANDIS, E. M., Qualitative properties of the solutions of a second-order nonlinear equation, Math. USSR-Sb. 63 (1989), 337-350.
21. KRYLOV, N. V. & SAFONOV, M. V., A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 161-175, 239.
22. LANDIS, E. M., Uniqueness theorems for the solution of the Dirichlet problem for second-order elliptic equations, Proc. Moscow Math. Soc. 42 (1981), 50-63.
23. 2 in a domain, Probab. Theory Related Fields 102 (1995), 393-432.
24. LOEWNER, C. & NIRENBERG, L., Partial differential equations invariant under conformal or projective transformations, in Contributions to Analysis, 245-272, New York-London: Academic Press 1974.
25. MARCUS, M. & VERON, L., Uniqueness and asymptotic behaviour of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), 237-274.
26. MARCUS, M. & VERON, L., The boundary trace of positive solutions of semilinear elliptic equations: the supercritical case, J. Math. Pures Appl. 77 (1998), 481-524.
27. MARCUS, M. & VERON, L., The boundary trace of positive solutions of semilinear elliptic equations: the subcritical case, Arch. Rational Mech. Anal. 144 (1998), 201-231.
28. NADIRASHVILI, N., Nonclassical solutions of fully nonlinear equations, Preprint.
29. PUCCI, C., Operatori ellittici estremanti, Ann. Mat. Pura Appl., 72 (1966), 141-170.
30. SAFONOV, M. V., Harnack's inequality for elliptic equations and Hölder property of their solutions, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 96 (1980), 272-287, 312.
31. SERRIN, J., Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247-302.
32. SERRIN, J., Isolated singularities of solutions of quasi-linear equations, Acta Math. 113 (1965), 219-240.
33. SERRIN, J., Removable singularities of solutions of elliptic equations, Arch. Rational Mech. Anal. 17 (1964), 67-78.
34. SERRIN, J., Removable singularities of solutions of elliptic equations. II, Arch. Rational Mech. Anal. 20 (1965), 163-169.
35. SERRIN, J., Singularities of solutions of nonlinear equations, 1965 Proc. Sympos. Appl. Math., Vol. XVII, 68-88, Amer. Math. Soc., Providence, R.I.
36. TRUDINGER, N. S., Hölder gradient estimates for fully nonlinear elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), 57-65.
37. TRUDINGER, N. S., Lectures on nonlinear elliptic equations of second order, Lecture notes published by Tokyo University, 1995.
38. VAZQUEZ, J. L. & VERON, L., Singularities of elliptic equations with an exponential nonlinearity, Math. Ann. 269 (1984), 119-135.
39. VERON, L., Singularities of solutions of second order quasilinear equations, Longman, Harlow, 1996.