Weak type-$(1,1)$ inequalities and regularity properties of adjoint and normalized adjoint solutions to linear nondivergence form operators with VMO coefficients
Luis Escauriaza
Source: Duke Math. J. Volume 74, Number 1
(1994), 177-201.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288015
Mathematical Reviews number (MathSciNet): MR1271469
Zentralblatt MATH identifier: 0818.42006
Digital Object Identifier: doi:10.1215/S0012-7094-94-07409-7
References
[B1] P. Bauman, Positive solutions of elliptic equations in nondivergence form and their adjoints, Ark. Mat. 22 (1984), no. 2, 153–173.
Mathematical Reviews (MathSciNet): MR86m:35008
Zentralblatt MATH: 0557.35033
Digital Object Identifier: doi:10.1007/BF02384378
[B2] P. Bauman, Equivalence of the Green's functions for diffusion operators in $\bf R\spn$: a counterexample, Proc. Amer. Math. Soc. 91 (1984), no. 1, 64–68.
Mathematical Reviews (MathSciNet): MR85d:35026
Zentralblatt MATH: 0574.35026
Digital Object Identifier: doi:10.2307/2045270
[B3] P. Bauman, A Wiener test for nondivergence structure, second-order elliptic equations, Indiana Univ. Math. J. 34 (1985), no. 4, 825–844.
Mathematical Reviews (MathSciNet): MR87b:35047
Zentralblatt MATH: 0583.35034
Digital Object Identifier: doi:10.1512/iumj.1985.34.34045
[BEF] B. Barcelo, L. Escauriaza, and E. Fabes, Gradient estimates at the boundary for solutions to nondivergence elliptic equations, Harmonic analysis and partial differential equations (Boca Raton, FL, 1988), Contemp. Math., vol. 107, Amer. Math. Soc., Providence, RI, 1990, pp. 1–12.
Mathematical Reviews (MathSciNet): MR91h:35068
Zentralblatt MATH: 0724.35038
[C] L. A. Caffarelli, Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math. (2) 130 (1989), no. 1, 189–213.
Mathematical Reviews (MathSciNet): MR90i:35046
Zentralblatt MATH: 0692.35017
Digital Object Identifier: doi:10.2307/1971480
JSTOR: links.jstor.org
[CFL] F. Chiarenza, M. Frasca, and P. Longo, Interior $W\sp 2,p$ estimates for nondivergence elliptic equations with discontinuous coefficients, Ricerche Mat. 40 (1991), no. 1, 149–168.
Mathematical Reviews (MathSciNet): MR93k:35051
Zentralblatt MATH: 0772.35017
[ChY] S. Chanillo and L. Yan Yan, Continuity of solutions of uniformly elliptic equations in $R^2$, preprint.
Mathematical Reviews (MathSciNet): MR1190215
Zentralblatt MATH: 0797.35031
Digital Object Identifier: doi:10.1007/BF02567065
[CW] S. Chanillo and R. L. Wheeden, Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal functions, Amer. J. Math. 107 (1985), no. 5, 1191–1226.
Mathematical Reviews (MathSciNet): MR87f:42045
Zentralblatt MATH: 0575.42026
Digital Object Identifier: doi:10.2307/2374351
JSTOR: links.jstor.org
[E] L. Escauriaza, $W^2,n$ a priori estimates for solutions to fully nonlinear equations, to appear in Indiana Univ. Math. J. 42 (1993), 413–423.
Mathematical Reviews (MathSciNet): MR1237053
Zentralblatt MATH: 0792.35020
Digital Object Identifier: doi:10.1512/iumj.1993.42.42019
[EK] L. Escauriaza and C. Kenig, Area integral estimates for solutions and normalized adjoint solutions to nondivergence form elliptic equation, to appear in Ark. Mat.
Mathematical Reviews (MathSciNet): MR1263555
[F] E. B. Fabes and D. W. Stroock, The $L\sp p$-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations, Duke Math. J. 51 (1984), no. 4, 997–1016.
Mathematical Reviews (MathSciNet): MR86g:35057
Zentralblatt MATH: 0567.35003
Digital Object Identifier: doi:10.1215/S0012-7094-84-05145-7
Project Euclid: euclid.dmj/1077304105
[FGMS] E. Fabes, N. Garofalo, S. Marin-Malave, and S. Salsa, Fatou theorems for some nonlinear elliptic equations, Rev. Mat. Iberoamericana 4 (1988), no. 2, 227–251.
Mathematical Reviews (MathSciNet): MR91e:35092
Zentralblatt MATH: 0703.35058
[GT] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR86c:35035
Zentralblatt MATH: 0562.35001
[GW] M. Grüter and K. O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), no. 3, 303–342.
Mathematical Reviews (MathSciNet): MR83h:35033
Zentralblatt MATH: 0485.35031
Digital Object Identifier: doi:10.1007/BF01166225
[J] J.-L. Journé, Calderón-Zygmund operators, pseudodifferential operators and the Cauchy integral of Calderón, Lecture Notes in Mathematics, vol. 994, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR85i:42021
Zentralblatt MATH: 0508.42021
[KS] 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.
Zentralblatt MATH: 0476.20031
[P] C. Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl. (4) 74 (1966), 15–30.
Mathematical Reviews (MathSciNet): MR35:5752
Zentralblatt MATH: 0144.35801
Digital Object Identifier: doi:10.1007/BF02416445
[Sa] D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391–405.
Mathematical Reviews (MathSciNet): MR51:13690
Zentralblatt MATH: 0319.42006
Digital Object Identifier: doi:10.2307/1997184
[S] E. W. Stredulinsky, Higher integrability from reverse Hölder inequalities, Indiana Univ. Math. J. 29 (1980), no. 3, 407–413.
Mathematical Reviews (MathSciNet): MR82m:26024
Zentralblatt MATH: 0442.35064
Digital Object Identifier: doi:10.1512/iumj.1980.29.29029
[ST] J. O. Strömberg and A. Torchinsky, Weighted Hardy spaces, Lecture Notes in Mathematics, vol. 1381, Springer-Verlag, Berlin, 1989.
Mathematical Reviews (MathSciNet): MR90j:42053
[SW] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971.
Mathematical Reviews (MathSciNet): MR46:4102
Zentralblatt MATH: 0232.42007
[W1] L. Wang, On the regularity theory of fully nonlinear parabolic equations. I, Comm. Pure Appl. Math. 45 (1992), no. 1, 27–76.
Mathematical Reviews (MathSciNet): MR92m:35126
Zentralblatt MATH: 0832.35025
Digital Object Identifier: doi:10.1002/cpa.3160450103
[W2] L. Wang, On the regularity theory of fully nonlinear parabolic equations. II, Comm. Pure Appl. Math. 45 (1992), no. 2, 141–178.
Mathematical Reviews (MathSciNet): MR92m:35127
Zentralblatt MATH: 0774.35042
Digital Object Identifier: doi:10.1002/cpa.3160450202
Duke Mathematical Journal