## Duke Mathematical Journal

### The $L^p$-integrability of Green’s functions and fundamental solutions for elliptic and parabolic equations

#### Article information

Source
Duke Math. J., Volume 51, Number 4 (1984), 997-1016.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077304105

Digital Object Identifier
doi:10.1215/S0012-7094-84-05145-7

Mathematical Reviews number (MathSciNet)
MR771392

Zentralblatt MATH identifier
0567.35003

#### Citation

Fabes, E. B.; Stroock, D. W. The $L^p$ -integrability of Green’s functions and fundamental solutions for elliptic and parabolic equations. Duke Math. J. 51 (1984), no. 4, 997--1016. doi:10.1215/S0012-7094-84-05145-7. https://projecteuclid.org/euclid.dmj/1077304105

#### 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.
• [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.
• [6] F. W. Gehring, The $L\spp$-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277.
• [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.
• [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.
• [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.
• [10] C. Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl. (4) 74 (1966), 15–30.
• [11] M. V. Safanov, Harnack's inequality for elliptic equations and the Hölder property of their solutions, J. Soviet Mathematics 21 (1983), 851–863.
• [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.
• [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.