Weak type-(1, 1) inequalities and regularity properties of adjoint and normalized adjoint solutions to linear nondivergence form operators with VMO coefficients

Duke Mathematical Journal

Volumn 74, Issue 1, 1994, Pages 177-201

  Escauriaza, Luis ^a,b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84974004982     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-94-07409-7     Document Type: Article

References (23)

1. P. BAUMAN, Positive solutions of elliptic equations in nondivergence form and their adjoints, Ark. Mat. 22 (1984), 153-173.
2. n: a counterexample, Proc. Amer. Math. Soc. 91 (1984), 64-68.
3. P. BAUMAN, A Wiener test for nondivergence structure second order elliptic equations, Indiana Univ. Math. J. 4 (1985), 825-844.
4. T. BARCELO, L. ESCAURIAZA, AND E. FABES, "Gradient estimates at the boundary for solutions to nondivergence elliptic equations" in Harmonic Analysis and Partial Differential Equations, Contemp. Math. 107, Amer. Math. Soc., Providence, 1990, 1-12.
5. L. CAFFARELLI, Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math. (2) 130 (1989), 189-213.
6. 2, p estimates for nondivergence elliptic equations with discontinuous coefficients, Richerche di Matemática, 40 (1991) 149-168.
7. 2, preprint.
8. S. CHANILLO AND R. L. WHEEDEN, Weighted Poincaré inequalities for solutions of degenerate elliptic equations, Amer. J. Math. 107 (1985), 1191-1226.
9. 2, n a priori estimates for solutions to fully nonlinear equations, to appear in Indiana Univ. Math. J. 42 (1993), 413-423.
10. L. ESCAURIAZA AND C. KENIG, Area integral estimates for solutions and normalized adjoint solutions to nondivergence form elliptic equation, to appear in Ark. Mat.
11. p-integrability of Greens functions and fundamental solutions for elliptic and parabolic equations, Duke Math. J. 51 (1984), 977-1016.
12. E. B. FABES, N. GAROFALO, S. MARIN MALAVE, AND S. SALSA, Fatou theorems for some nonlinear elliptic equations, Rev. Mat. Iberoamericana 4 (1988), 227-251.
13. D. GILBARG AND N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss. 224, Springer-Verlag, New York, 1983.
14. M. GRÜTER AND K. O. WIDMAN, The Green’s function for uniformly elliptic equations, Manuscripta Math. 37 (1987), 303-342.
15. J. L. JOURNÉ, Calderón-Zygmund Operators, Pseudo-Differential Operators, and the Cauchy Integral of Calderón, Lecture Notes in Math. 994, Springer-Verlag, Berlin, 1983.
16. N. V. KRYLOV AND M. V. SAFONOV, An estimate on the probability that a diffusion hits a set of positive measure, Soviet Math. J. 20 (1979), 253-256.
17. C. Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl. (4) 74 (1966), 15-30.
18. D. SARASON, Functions of vanishing mean oscilation, Trans. Amer. Math. Soc. 207 (1975), 391-405.
19. E. W. STREDULINSKY, Higher integrability from inverse Hölder inequalities, Indiana Univ. Math. J. 29 (1980), 407-413.
20. J. O. SROMBERG AND A. TORCHINSKY, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer-Verlag, Berlin, 1984.
21. E. M. STEIN AND G. WEISS, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Series 32, Princeton Univ. Press, Princeton, New Jersey, 1971.
22. L. WANG, On the regularity of solutions to fully-nonlinear parabolic equatons, I, Comm. Pure Appl. Math. 45 (1992), 144-169.
23. L. WANG, On the regularity of solutions to fully-nonlinear parabolic equations, II, Comm. Pure Appl. Math. 45 (1992), 27-96.