Estimates of the fundamental solution for an elliptic equation in divergence form with drift
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 7-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a second-order linear divergence-form elliptic equation with uniformly elliptic measurable principal coefficients and with drift we establish a condition on lower order coefficients that guarantees classical two-sided bounds of the fundamental solution.
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Yu. A. Alkhutov; M. D. Surnachev. Estimates of the fundamental solution for an elliptic equation in divergence form with drift. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 7-35. http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a0/

[1] W. Littman, G. Stampacchia, H. F. Weinberger, “Regular points for elliptic equations with discontinuous coefficients”, Ann. Scuola Norm. Sup. Pisa, 17 (1963), 45–79 | MR

[2] G. Stampacchia, “Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus”, Annales de l'Institut Fourier, 15:1 (1965), 189–257 | DOI | MR | Zbl

[3] Y. Pinchover, “On the equivalence of Green functions of second order elliptic equation in $\mathbb{R}^n$”, Diff. Integral Equations, 5:3 (1992), 481–493 | MR | Zbl

[4] Qi Zhang, “A Harnack inequality for the equation $\nabla (a\nabla u)+b\nabla u=0$, when $|b| \in K_{n+1}$”, Manuscripta Math., 89 (1995), 61–77 | DOI | MR

[5] Qi S. Zhang, “Gaussian bounds for the fundamental solutions of $\nabla (A\nabla u)+B\nabla u -u_t=0$”, Manuscripta Math., 93 (1997), 381–390 | DOI | MR | Zbl

[6] V. Kondratiev, V. Liskevich, Z. Sobol, O. Us, “Estimates of heat kernels for a class of second-order elliptic operators with applications to semi-linear inequalitites in exterior domains”, J. London Math. Soc., 69:2 (2004), 107–127 | DOI | MR | Zbl

[7] V. Kozlov, A. I. Nazarov, A comparison theorem for nonsmooth linear operators, 24 Jan 2019, arXiv: 1901.08631v1

[8] K. Kurata, “Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order”, Indiana University Math. J., 43:2 (1994), 411–440 | DOI | MR | Zbl

[9] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966

[10] E. M. Landis, Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971