Schauder estimates for parabolic nondivergence operators of Hörmander type
Tài liệu tham khảo
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