W1,P-interior estimates for solutions of fully nonlinear, uniformly elliptic equations

Advances in Differential Equations

Volumn 2, Issue 6, 1997, Pages 1005-1027

  Świech, Andrzej ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

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EID: 0003282543     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. X. Cabré, On the Alexandroff-Bakelman-Pucci estimate and the reversed Hölder inequality for solutions of elliptic and parabolic equations, Comm. Pure Appl. Math., 48 (1995), 539-570.
2. L. Caffarelli, Interior a priori estimates for solutions of fully non-linear equations, Ann. Math., 130 (1989), 189-213.
3. L. Caffarelli and X. Cabré, "Fully nonlinear elliptic equations," AMS Colloquium Publications, vol. 43, 1995.
4. L. Caffarelli, M.G. Crandall, M. Kocan, and A. Świech, On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math., 49 (1996), 365-397.
5. M.G. Crandall, H. Ishii, and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67.
6. M.G. Crandall, M. Kocan, P. Soravia, and A. Świech, On the equivalence of various weak notions of solutions of elliptic PDEs with measurable ingredients, Progress in Elliptic and Parabolic Partial Differential Equations (A. Alvino et al. eds.), Pitman Research Notes in Math. vol. 350, 1996, 136-162.
7. 2,n a priori estimates for solutions to fully non-linear equations, Indiana Univ. Math. J., 42 (1993), 413-423.
8. L.C. Evans, A convergence theorem for solutions of nonlinear second order elliptic equations, Indiana Univ. Math. J., 27 (1978), 875-887.
9. L.C. Evans, Classical solutions of fully nonlinear, convex, second order elliptic equations, Comm. Pure Appl. Math., 35 (1982), 333-363.
10. L.C. Evans, Some estimates for nondivergence structure second order elliptic equations, Trans. Amer. Math. Soc., 287 (1985), 701-712.
11. p integrability of Green's functions and fundamental solutions for elliptic and parabolic equations, Duke J. Math., 51 (1984), 997-1016.
12. P. Fok, Ph.D. Thesis, UCSB, 1996.
13. D. Gilbarg and N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", 2nd ed., Springer-Verlag, New York, 1983.
14. H. Ishii and P.L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Diff. Eq., 83 (1990), 26-78.
15. R. Jensen, Uniqueness criteria for viscosity solutions of fully nonlinear elliptic partial differential equations, Indiana Univ. Math. J., 38 (1989), 629-667.
16. N.V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR, 46 (1982), 487-523 (Russian), English translation in Math. USSR Izv., 20 (1983).
17. N.V. Krylov, "Nonlinear elliptic and parabolic equations of the second order," Reidel Pub. Co., Dordrecht, 1987.
18. N.V. Krylov and M.V. Safonov, Certain properties of parabolic equations with measurable coefficients, Math. USSR Izvestiya, 16 (1981), 151-164.
19. p estimates for elliptic equations of nondivergent type, Proc. Amer. Math. Soc., 96 (1986), 447-451.
20. C. Pucci, Operatori ellittici estremali, Ann. Mat. Pura Appl., 72 (1966), 141-170.
21. N.S. Trudinger, Comparison principles and pointwise estimates for viscosity solutions, Rev. Mat. Iberoamericana, 4 (1988), 453-468.
22. N.S. Trudinger, Hölder gradient estimates for fully nonlinear elliptic equations, Proc. Royal Soc. Edinburgh, 108A (1988), 57-65.
23. N.S. Trudinger, On regularity and existence of viscosity solutions of non-linear second order elliptic equations, Partial differential equations and the calculus of variation: Essays in honor of Ennio De Giorgi, Birkhäuser, Boston, 1989, 939-957.
24. L. Wang, On the regularity of fully nonlinear parabolic equations: I, Comm. Pure Appl. Math., 45 (1992), 27-76.
25. L. Wang, On the regularity of fully nonlinear parabolic equations: II, Comm. Pure Appl. Math., 45 (1992), 141-178.
26. W.P. Ziemer, "Weakly Differentiable Functions," Springer-Verlag, 1989.