The $L^p$-integrability of Green’s functions and fundamental solutions for elliptic and parabolic equations
E. B. Fabes and D. W. Stroock
Source: Duke Math. J. Volume 51, Number 4
(1984), 997-1016.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077304105
Mathematical Reviews number (MathSciNet): MR771392
Zentralblatt MATH identifier: 0567.35003
Digital Object Identifier: doi:10.1215/S0012-7094-84-05145-7
References
[1] A. D. Alexandrov, Uniqueness conditions and estimates of the solution of Dirichlet's problem, Vestn. Leningr. Un.-ta. 13 (1963), 5–29.
[2] P. Bauman, Properties of nonnegative solutions of second-order elliptic equations and their adjoints, Ph.D. thesis, University of Minnesota, Minneapolis, Minnesota, 1982.
[3] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250.
Mathematical Reviews (MathSciNet): MR50:10670
Zentralblatt MATH: 0291.44007
[4] L. C. Evans, Some estimates for nondivergence structure, second order equations, preprint.
[5] E. B. Fabes and C. E. Kenig, Examples of singular parabolic measures and singular transition probability densities, Duke Math. J. 48 (1981), no. 4, 845–856.
Mathematical Reviews (MathSciNet): MR86j:35081
Zentralblatt MATH: 0482.35021
Digital Object Identifier: doi:10.1215/S0012-7094-81-04846-8
Project Euclid: euclid.dmj/1077314934
[6] F. W. Gehring, The $L\spp$-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277.
Mathematical Reviews (MathSciNet): MR53:5861
Zentralblatt MATH: 0258.30021
Digital Object Identifier: doi:10.1007/BF02392268
[7] N. V. Krylov, Sequences of convex functions, and estimates of the maximum of the solution of a parabolic equation, Sibirsk. Mat. Ž. 17 (1976), no. 2, 290–303, 478, English translation in Siberian Math. J. 17 (1967), 266–236.
Mathematical Reviews (MathSciNet): MR54:8033
Zentralblatt MATH: 0354.35052
[8] N. V. Krylov and M. V. Safanov, A certain property of solutions of parabolic equations with measurable coefficients, Math. USSR Izvestija 16 (1981), 151–164, English translation in Izv. Akad. Nauk SSSR 44 (1980), 81–98.
Zentralblatt MATH: 0464.35035
[9] P. L. Lions, Some recent results in the optimal control of diffusion processes, Cahiers de Mathematiques de la Decision, No. 8302, Ceremade (1983), preprint.
Mathematical Reviews (MathSciNet): MR780764
Zentralblatt MATH: 0549.93070
[10] 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
[11] M. V. Safanov, Harnack's inequality for elliptic equations and the Hölder property of their solutions, J. Soviet Mathematics 21 (1983), 851–863.
Zentralblatt MATH: 0511.35029
[12] D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 233, Springer-Verlag, Berlin, 1979.
Mathematical Reviews (MathSciNet): MR81f:60108
Zentralblatt MATH: 0426.60069
[13] N. S. Trudinger, Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations, Invent. Math. 61 (1980), no. 1, 67–79.
Mathematical Reviews (MathSciNet): MR81m:35058
Zentralblatt MATH: 0453.35028
Digital Object Identifier: doi:10.1007/BF01389895
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