Interior regularity for weak solutions of ultraparabolic equations in divergence form with discontinuous coefficients

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1. BRAMANTI, M.- CERUTTI, M. C., $W_p^{1,2}$ solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients, Comm. Partial Differential Equations, 18 (1993), 1735-1763. Zbl0816.35045MR1239929
2. BRAMANTI, M.- CERUTTI, M. C.- MANFREDINI, M., $L^p$ estimates for some ultraparabolic operators with discontinuous coefficients, J. Math. Anal. Appl., 200 (1996), 332-354. Zbl0922.47039MR1391154
3. CHIARENZA, F.- FRASCA, M.- LONGO, P., Interior $W_p^{1,2}$ estimates for non divergence elliptic equations with discontinuous coefficients, Ricerche Mat., 40 (1991), 149-168. Zbl0772.35017MR1191890
4. DI FAZIO, G., $L^p$ estimates for divergence form elliptic equations with discontinuous coefficients, Boll. Un. Mat. Ital. A (7), 10 (1996), 409-420. Zbl0865.35048MR1405255
5. FABES, E. B.- RIVIÈRE, N. M., Singular integrals with mixed homogeneity, Studia Math., 27 (1966), 19-38. Zbl0161.32403MR209787
6. LANCONELLI, E.- POLIDORO, S., On a class of hypoelliptic evolution operators, Rend. Sem. Mat. Univ. Politec. Torino, 52 (1994), 29-63. Zbl0811.35018MR1289901
7. MANFREDINI, M., The Dirichlet problem for a class of ultraparabolic equations, to appear on Differential Integral Equations. Zbl1023.35518
8. MOSER, J., A Harnack inequality for parabolic differental equations, Comm. Pure Appl. Math., 17 (1964), 101-134, and correction in Comm. Pure Appl. Math., 20 (1967), 231-236. Zbl0149.07001MR159139
9. NASH, J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), 931-954. Zbl0096.06902MR100158
10. POLIDORO, S., On a class of ultraparabolic operators of Kolmogorov-Fokker-Planck type, Le Matematiche, 49 (1994), 53-105. Zbl0845.35059MR1386366
11. POLIDORO, S., A global lower bound for the fundamental solution of Kolmogorov-Fokker-Planck equations, Arch. Rational Mech. Anal., 137 (1997), 321-340. Zbl0887.35086MR1463798
12. POLIDORO, S., Uniqueness and representation theorems for solutions of Kolmogorov-Fokker-Planck equations, Rend. Mat. Appl. (7), 15 (1995), 535-560. Zbl0847.35075MR1387312
13. STEIN, E. M., Armonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, New Jersey, 1993. Zbl0821.42001MR1232192
14. FOLLAND, G. B., Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv for Math., 13 (1975), 161-207. Zbl0312.35026MR494315