Schauder estimates for parabolic nondivergence operators of Hörmander type

Journal of Differential Equations - Tập 234 - Trang 177-245 - 2007
Marco Bramanti1, Luca Brandolini2
1Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133 Milano, Italy
2Dipartimento di Ingegneria Gestionale e dell'Informazione, Università degli Studi di Bergamo, Viale Marconi 5, 24044 Dalmine BG, Italy

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Bonfiglioli, 2002, Uniform Gaussian estimates of the fundamental solutions for heat operators on Carnot groups, Adv. Differential Equations, 7, 1153, 10.57262/ade/1356651633 Bonfiglioli, 2004, Fundamental solutions for non-divergence form operators on stratified groups, Trans. Amer. Math. Soc., 356, 2709, 10.1090/S0002-9947-03-03332-4 Bony, 1969, Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble), 19, 277, 10.5802/aif.319 Bonfiglioli, 2006, Maximum principle and propagation for intrinsically regular solutions of differential inequalities structured on vector fields, J. Math. Anal. Appl., 322, 886, 10.1016/j.jmaa.2005.09.067 Bramanti, 2000, Lp-estimates for uniformly hypoelliptic operators with discontinuous coefficients on homogeneous groups, Rend. Sem. Mat. Univ. Politec. Torino, 58, 389 Bramanti, 2000, Lp-estimates for nonvariational hypoelliptic operators with VMO coefficients, Trans. Amer. Math. Soc., 352, 781, 10.1090/S0002-9947-99-02318-1 Bramanti, 2005, Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs, Rev. Mat. Iberoamericana, 21, 511, 10.4171/RMI/428 M. Bramanti, L. Brandolini, E. Lanconelli, F. Uguzzoni, Non-divergence equations structured on Hörmander vector fields: Heat kernels and Harnack inequalities, preprint, 2006 Caffarelli, 1989, Interior a-priori estimates for solutions of fully nonlinear equations, Ann. of Math. (2), 130, 189, 10.2307/1971480 Calderón, 1957, Singular integral operators and differential equations, Amer. J. Math., 79, 901, 10.2307/2372441 Campanato, 1963, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 17, 175 Capogna, 2003, Pointwise Schauder estimates for second order linear equations in Carnot groups, vol. 320, 45 Chen, 1998, Second Order Elliptic Equations and Elliptic Systems, vol. 174 Citti, 2006, A cortical based model of perceptual completion in the roto-translation space, J. Math. Imaging Vision, 24, 307, 10.1007/s10851-005-3630-2 Coifman, 1971, Analyse Harmonique Non Commutative sur Certains Espaces Homogènes, vol. 242 Folland, 1975, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Math., 13, 161, 10.1007/BF02386204 Gatto, 1990, Fractional integrals on spaces of homogeneous type, vol. 122, 171 Gatto, 1992, On molecules and fractional integrals on spaces of homogeneous type with finite measure, Studia Math., 103, 25, 10.4064/sm-103-1-25-39 Gatto, 1996, On fractional differentiation and integration on spaces of homogeneous type, Rev. Mat. Iberoamericana, 12, 111, 10.4171/RMI/196 Hörmander, 1967, Hypoelliptic second order differential equations, Acta Math., 119, 147, 10.1007/BF02392081 Korányi, 1971, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 25, 575 Krylov, 1996, Lectures on Elliptic and Parabolic Equations in Hölder Spaces, vol. 12 Kusuoka, 1987, Applications of the Malliavin calculus. III, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 34, 391 Macías, 1979, Lipschitz functions on spaces of homogeneous type, Adv. Math., 33, 257, 10.1016/0001-8708(79)90012-4 Meyers, 1964, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc., 15, 717 Montanari, 2003, Hölder a-priori estimates for second order tangential operators on CR manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2, 345 Montanari, 2004, Pseudoconvex fully nonlinear partial differential operators, strong comparison theorems, J. Differential Equations, 202, 306, 10.1016/j.jde.2004.03.017 Nagel, 1985, Balls and metrics defined by vector fields I: Basic properties, Acta Math., 155, 130, 10.1007/BF02392539 Rothschild, 1976, Hypoelliptic differential operators and nilpotent groups, Acta Math., 137, 247, 10.1007/BF02392419 Sanchez-Calle, 1984, Fundamental solutions and geometry of sum of squares of vector fields, Invent. Math., 78, 143, 10.1007/BF01388721 Spanne, 1965, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 19, 593 Stein, 1993 Xu, 1992, Regularity for quasilinear second-order subelliptic equations, Comm. Pure Appl. Math., 45, 77, 10.1002/cpa.3160450104