Geodesic
Levi’s parametrix for some sub-elliptic non-divergence form operators
Bonfiglioli, Andrea1 ; Lanconelli, Ermanno1 ; Uguzzoni, Francesco1
1 Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 10-18 Cet article a éte moissonné depuis la source American Mathematical Society

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We construct the fundamental solutions for the sub-elliptic operators in non-divergence form ${\textstyle \sum _{i,j}} a_{i,j}(x,t) X_iX_j-\partial _t$ and ${\textstyle \sum _{i,j}}a_{i,j}(x) X_iX_j$, where the $X_i$’s form a stratified system of Hörmander vector fields and $a_{i,j}$ are Hölder continuous functions belonging to a suitable class of ellipticity.
DOI : 10.1090/S1079-6762-03-00107-0

Bonfiglioli, Andrea 1 ; Lanconelli, Ermanno 1 ; Uguzzoni, Francesco 1

1 Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy 
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Bonfiglioli, Andrea; Lanconelli, Ermanno; Uguzzoni, Francesco. Levi’s parametrix for some sub-elliptic non-divergence form operators. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 10-18. doi: 10.1090/S1079-6762-03-00107-0

[1] Bramanti, Marco, Brandolini, Luca 𝐿^{𝑝} estimates for nonvariational hypoelliptic operators with VMO coefficients Trans. Amer. Math. Soc. 2000 781 822

[2] Capogna, Luca Regularity for quasilinear equations and 1-quasiconformal maps in Carnot groups Math. Ann. 1999 263 295

[3] Capogna, Luca, Danielli, Donatella, Garofalo, Nicola Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations Amer. J. Math. 1996 1153 1196

[4] Citti, Giovanna, Garofalo, Nicola, Lanconelli, Ermanno Harnack’s inequality for sum of squares of vector fields plus a potential Amer. J. Math. 1993 699 734

[5] Folland, G. B. Subelliptic estimates and function spaces on nilpotent Lie groups Ark. Mat. 1975 161 207

[6] Franchi, B., Lu, G., Wheeden, R. L. Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations Potential Anal. 1995 361 375

[7] Hörmander, Lars Hypoelliptic second order differential equations Acta Math. 1967 147 171

[8] Huisken, Gerhard, Klingenberg, Wilhelm Flow of real hypersurfaces by the trace of the Levi form Math. Res. Lett. 1999 645 661

[9] Jerison, David, Lee, John M. The Yamabe problem on CR manifolds J. Differential Geom. 1987 167 197

[10] Jerison, David S., Sánchez-Calle, Antonio Estimates for the heat kernel for a sum of squares of vector fields Indiana Univ. Math. J. 1986 835 854

[11] Kusuoka, S., Stroock, D. Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator Ann. of Math. (2) 1988 165 189

[12] Lu, Guozhen Existence and size estimates for the Green’s functions of differential operators constructed from degenerate vector fields Comm. Partial Differential Equations 1992 1213 1251

[13] Montanari, A. Real hypersurfaces evolving by Levi curvature: smooth regularity of solutions to the parabolic Levi equation Comm. Partial Differential Equations 2001 1633 1664

[14] Montgomery, Richard A tour of subriemannian geometries, their geodesics and applications 2002

[15] Petitot, Jean, Tondut, Yannick Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux Math. Inform. Sci. Humaines 1999 5 101

[16] Rothschild, Linda Preiss, Stein, E. M. Hypoelliptic differential operators and nilpotent groups Acta Math. 1976 247 320

[17] Slodkowski, Zbigniew, Tomassini, Giuseppe Weak solutions for the Levi equation and envelope of holomorphy J. Funct. Anal. 1991 392 407

[18] Varopoulos, N. Th., Saloff-Coste, L., Coulhon, T. Analysis and geometry on groups 1992

[19] Xu, Chao Jiang Regularity for quasilinear second-order subelliptic equations Comm. Pure Appl. Math. 1992 77 96

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