Nicola Garofalo
Publications listed in MathSciNet
| [1] | Luca Capogna and Nicola Garofalo. Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces. J. Geom. Anal., 16(3):457-497, 2006. |
| [2] | Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu. Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces. Mem. Amer. Math. Soc., 182(857):x+119, 2006. |
| [3] | Nicola Garofalo and Federico Tournier. New properties of convex functions in the Heisenberg group. Trans. Amer. Math. Soc., 358(5):2011-2055 (electronic), 2006. |
| [4] | Nicola Garofalo and Dimiter Vassilev. Strong unique continuation for generalized Baouendi-Grushin operators. In Advances in analysis, pages 255-263. World Sci. Publ., Hackensack, NJ, 2005. |
| [5] | D. Danielli, N. Garofalo, D. M. Nhieu, and F. Tournier. The theorem of Busemann-Feller-Alexandrov in Carnot groups. Comm. Anal. Geom., 12(4):853-886, 2004. |
| [6] | Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu. Notions of convexity in Carnot groups. Comm. Anal. Geom., 11(2):263-341, 2003. |
| [7] | Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu. On the best possible character of the LQ norm in some a priori estimates for non-divergence form equations in Carnot groups. Proc. Amer. Math. Soc., 131(11):3487-3498 (electronic), 2003. |
| [8] | Donatella Danielli, Nicola Garofalo, and Sandro Salsa. Variational inequalities with lack of ellipticity. I. Optimal interior regularity and non-degeneracy of the free boundary. Indiana Univ. Math. J., 52(2):361-398, 2003. |
| [9] | Luca Capogna and Nicola Garofalo. Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type. J. Eur. Math. Soc. (JEMS), 5(1):1-40, 2003. |
| [10] | Donatella Danielli and Nicola Garofalo. Properties of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions. Calc. Var. Partial Differential Equations, 15(4):451-491, 2002. |
| [11] | Luca Capogna, Nicola Garofalo, and Duy-minh Nhieu. Properties of harmonic measures in the Dirichlet problem for nilpotent Lie groups of Heisenberg type. Amer. J. Math., 124(2):273-306, 2002. |
| [12] | Nicola Garofalo and Elena Sartori. Symmetry in a free boundary problem for degenerate parabolic equations on unbounded domains. Proc. Amer. Math. Soc., 129(12):3603-3610 (electronic), 2001. |
| [13] | Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu. Sub-elliptic Besov spaces and the characterization of traces on lower dimensional manifolds. In Harmonic analysis and boundary value problems (Fayetteville, AR, 2000), volume 277 of Contemp. Math., pages 19-37. Amer. Math. Soc., Providence, RI, 2001. |
| [14] | Nicola Garofalo and Dimiter Vassilev. Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type. Duke Math. J., 106(3):411-448, 2001. |
| [15] | Luca Capogna, Nicola Garofalo, and Duy-Minh Nhieu. Examples of uniform and NTA domains in Carnot groups. In Proceedings on Analysis and Geometry (Russian) (Novosibirsk Akademgorodok, 1999), pages 103-121. Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000. |
| [16] | Nicola Garofalo and Dimiter Vassilev. Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups. Math. Ann., 318(3):453-516, 2000. |
| [17] | Nicola Garofalo and Dimiter Vassilev. The non-linear Dirichlet problem and the CR Yamabe problem. Matematiche (Catania), 54(suppl.):75-93, 1999. Boundary value problems for elliptic and parabolic operators (Catania, 1998). |
| [18] | Nicola Garofalo and Elena Sartori. Symmetry in exterior boundary value problems for quasilinear elliptic equations via blow-up and a priori estimates. Adv. Differential Equations, 4(2):137-161, 1999. |
| [19] | Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu. Trace inequalities for Carnot-Carathéodory spaces and applications. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 27(2):195-252 (1999), 1998. |
| [20] | Luca Capogna and Nicola Garofalo. Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics. J. Fourier Anal. Appl., 4(4-5):403-432, 1998. |
| [21] | Luca Capogna, Nicola Garofalo, and Duy-Minh Nhieu. A version of a theorem of Dahlberg for the subelliptic Dirichlet problem. Math. Res. Lett., 5(4):541-549, 1998. |
| [22] | Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu. Isoperimetric and trace inequalities with respect to Carnot-Carathéodory metrics. In Geometry Seminars, 1996-1997 (Italian) (Bologna), pages 51-62. Univ. Stud. Bologna, Bologna, 1998. |
| [23] | Nicola Garofalo and Duy-Minh Nhieu. Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces. J. Anal. Math., 74:67-97, 1998. |
| [24] | Donatella Danielli and Nicola Garofalo. Geometric properties of solutions to subelliptic equations in nilpotent Lie groups. In Reaction diffusion systems (Trieste, 1995), volume 194 of Lecture Notes in Pure and Appl. Math., pages 89-105. Dekker, New York, 1998. |
| [25] | Harold Donnelly and Nicola Garofalo. Schrödinger operators on manifolds, essential self-adjointness, and absence of eigenvalues. J. Geom. Anal., 7(2):241-257, 1997. |
| [26] | Luca Capogna, Donatella Danielli, and Nicola Garofalo. Subelliptic mollifiers and a basic pointwise estimate of Poincaré type. Math. Z., 226(1):147-154, 1997. |
| [27] | Luca Capogna, Donatella Danielli, and Nicola Garofalo. Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations. Amer. J. Math., 118(6):1153-1196, 1996. |
| [28] | Nicola Garofalo and Duy-Minh Nhieu. Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces. Comm. Pure Appl. Math., 49(10):1081-1144, 1996. |
| [29] | Nicola Garofalo and Zhongwei Shen. Absence of positive eigenvalues for a class of subelliptic operators. Math. Ann., 304(4):701-715, 1996. |
| [30] | Luca Capogna and Nicola Garofalo. Nontangentially accessible domains for Carnot-Carathéodory metrics and a Fatou type theorem. C. R. Acad. Sci. Paris Sér. I Math., 321(12):1565-1570, 1995. |
| [31] | Luca Capogna, Donatella Danielli, and Nicola Garofalo. The geometric Sobolev embedding for vector fields and the isoperimetric inequality. Comm. Anal. Geom., 2(2):203-215, 1994. |
| [32] | Luis Caffarelli, Nicola Garofalo, and Fausto Segàla. A gradient bound for entire solutions of quasi-linear equations and its consequences. Comm. Pure Appl. Math., 47(11):1457-1473, 1994. |
| [33] | Luca Capogna, Donatella Danielli, and Nicola Garofalo. An isoperimetric inequality and the geometric Sobolev embedding for vector fields. Math. Res. Lett., 1(2):263-268, 1994. |
| [34] | N. Garofalo and Z. Shen. Carleman estimates for a subelliptic operator and unique continuation. Ann. Inst. Fourier (Grenoble), 44(1):129-166, 1994. |
| [35] | Nicola Garofalo and Fausto Segàla. Univalent functions and the Pompeiu problem. Trans. Amer. Math. Soc., 346(1):137-146, 1994. |
| [36] | L. Capogna, D. Danielli, and N. Garofalo. Subelliptic mollifiers and a characterization of Rellich and Poincaré domains. Rend. Sem. Mat. Univ. Politec. Torino, 51(4):361-386 (1994), 1993. Partial differential equations, I (Turin, 1993). |
| [37] | Luca Capogna, Donatella Danielli, and Nicola Garofalo. An embedding theorem and the Harnack inequality for nonlinear subelliptic equations. Comm. Partial Differential Equations, 18(9-10):1765-1794, 1993. |
| [38] | Nicola Garofalo. Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension. J. Differential Equations, 104(1):117-146, 1993. |
| [39] | Giovanna Citti, Nicola Garofalo, and Ermanno Lanconelli. Harnack's inequality for sum of squares of vector fields plus a potential. Amer. J. Math., 115(3):699-734, 1993. |
| [40] | Luca Capogna, Donatella Danielli, and Nicola Garofalo. Embedding theorems and the Harnack inequality for solutions of nonlinear subelliptic equations. C. R. Acad. Sci. Paris Sér. I Math., 316(8):809-814, 1993. |
| [41] | Nicola Garofalo and Fausto Segàla. Another step toward the solution of the Pompeiu problem in the plane. Comm. Partial Differential Equations, 18(3-4):491-503, 1993. |
| [42] | Harold Donnelly and Nicola Garofalo. Riemannian manifolds whose Laplacians have purely continuous spectrum. Math. Ann., 293(1):143-161, 1992. |
| [43] | Nicola Garofalo and Ermanno Lanconelli. Existence and nonexistence results for semilinear equations on the Heisenberg group. Indiana Univ. Math. J., 41(1):71-98, 1992. |
| [44] | Nicola Garofalo. Unique continuation for degenerate elliptic equations. In Partial differential equations with minimal smoothness and applications (Chicago, IL, 1990), volume 42 of IMA Vol. Math. Appl., pages 139-148. Springer, New York, 1992. |
| [45] | Nicola Garofalo and Fausto Segàla. Asymptotic expansions for a class of Fourier integrals and applications to the Pompeiu problem. J. Analyse Math., 56:1-28, 1991. |
| [46] | Nicola Garofalo and Fausto Segàla. New results on the Pompeiu problem. Trans. Amer. Math. Soc., 325(1):273-286, 1991. |
| [47] | E. Fabes, N. Garofalo, and S. Salsa. A control on the set where a Green's function vanishes. Colloq. Math., 60/61(2):637-647, 1990. |
| [48] | Nicola Garofalo and Fausto Segàla. Estimates of the fundamental solution and Wiener's criterion for the heat equation on the Heisenberg group. Indiana Univ. Math. J., 39(4):1155-1196, 1990. |
| [49] | Nicola Garofalo and Fausto Segàla. Estimations de la solution fondamentale pour l'opérateur de la chaleur sur le groupe de Heisenberg et applications au critère de Wiener. C. R. Acad. Sci. Paris Sér. I Math., 311(6):321-323, 1990. |
| [50] | N. Garofalo and E. Lanconelli. Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation. Ann. Inst. Fourier (Grenoble), 40(2):313-356, 1990. |
| [51] | Nicola Garofalo and Ermanno Lanconelli. Zero-order perturbations of the subelliptic Laplacian on the Heisenberg group and their uniqueness properties. Bull. Amer. Math. Soc. (N.S.), 23(2):501-512, 1990. |
| [52] | Eugene B. Fabes, Nicola Garofalo, and Fang-Hua Lin. A partial answer to a conjecture of B. Simon concerning unique continuation. J. Funct. Anal., 88(1):194-210, 1990. |
| [53] | Nicola Garofalo and Ermanno Lanconelli. Level sets of the fundamental solution and Harnack inequality for degenerate equations of Kolmogorov type. Trans. Amer. Math. Soc., 321(2):775-792, 1990. |
| [54] | N. Garofalo. A new result on the Pompeiu problem. Rend. Sem. Mat. Univ. Politec. Torino, (Special Issue):25-38 (1990), 1989. Conference on Partial Differential Equations and Geometry (Torino, 1988). |
| [55] | E. Fabes, N. Garofalo, S. Marín-Malave, and S. Salsa. A Fatou theorem for the p-Laplacian. In Symposia Mathematica, Vol.XXX (Cortona, 1988), Sympos. Math., XXX, pages 27-44. Academic Press, London, 1989. |
| [56] | Eugene B. Fabes, Nicola Garofalo, and Ermanno Lanconelli. Wiener's criterion for divergence form parabolic operators with C1-Dini continuous coefficients. Duke Math. J., 59(1):191-232, 1989. |
| [57] | Giovanni Alessandrini and Nicola Garofalo. Symmetry for degenerate parabolic equations. Arch. Rational Mech. Anal., 108(2):161-174, 1989. |
| [58] | Nicola Garofalo and Ermanno Lanconelli. Asymptotic behavior of fundamental solutions and potential theory of parabolic operators with variable coefficients. Math. Ann., 283(2):211-239, 1989. |
| [59] | Nicola Garofalo and John L. Lewis. A symmetry result related to some overdetermined boundary value problems. Amer. J. Math., 111(1):9-33, 1989. |
| [60] | E. Fabes, N. Garofalo, S. Marín-Malave, and S. Salsa. Fatou theorems for some nonlinear elliptic equations. Rev. Mat. Iberoamericana, 4(2):227-251, 1988. |
| [61] | Nicola Garofalo. New estimates of the fundamental solution and Wiener's criterion for parabolic equations with variable coefficients. In Calculus of variations and partial differential equations (Trento, 1986), volume 1340 of Lecture Notes in Math., pages 70-83. Springer, Berlin, 1988. |
| [62] | Nicola Garofalo and Ermanno Lanconelli. Wiener's criterion for parabolic equations with variable coefficients and its consequences. Trans. Amer. Math. Soc., 308(2):811-836, 1988. |
| [63] | Nicola Garofalo and Fang-Hua Lin. Unique continuation for elliptic operators: a geometric-variational approach. Comm. Pure Appl. Math., 40(3):347-366, 1987. |
| [64] | E. B. Fabes and N. Garofalo. Mean value properties of solutions to parabolic equations with variable coefficients. J. Math. Anal. Appl., 121(2):305-316, 1987. |
| [65] | F. Chiarenza, E. Fabes, and N. Garofalo. Harnack's inequality for Schrödinger operators and the continuity of solutions. Proc. Amer. Math. Soc., 98(3):415-425, 1986. |
| [66] | Eugene B. Fabes, Nicola Garofalo, and Sandro Salsa. A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations. Illinois J. Math., 30(4):536-565, 1986. |
| [67] | Nicola Garofalo. Uniqueness in the past for parabolic equations with strongly singular potentials. Boll. Un. Mat. Ital. A (6), 5(2):263-271, 1986. |
| [68] | Nicola Garofalo and Fang-Hua Lin. Monotonicity properties of variational integrals, Ap weights and unique continuation. Indiana Univ. Math. J., 35(2):245-268, 1986. |
| [69] | Nicola Garofalo and Paul B. Garrett. Ap-weight properties of real analytic functions in Rn. Proc. Amer. Math. Soc., 96(4):636-642, 1986. |
| [70] | Nicola Garofalo and Sandro Salsa. The initial-Dirichlet problem for parabolic equations in nonsmooth domains. Boll. Un. Mat. Ital. B (6), 4(2):443-471, 1985. |
| [71] | Eugene B. Fabes and Nicola Garofalo. Parabolic B.M.O. and Harnack's inequality. Proc. Amer. Math. Soc., 95(1):63-69, 1985. |
| [72] | Eugene B. Fabes, Nicola Garofalo, and Sandro Salsa. Comparison theorems for temperatures in noncylindrical domains. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 77(1-2):1-12 (1985), 1984. |
| [73] | Nicola Garofalo. Second order parabolic equations in nonvariational forms: boundary Harnack principle and comparison theorems for nonnegative solutions. Ann. Mat. Pura Appl. (4), 138:267-296, 1984. |
| [74] | Nicola Garofalo. Dirichlet problem for singular parabolic equations: uniqueness of smooth flat solutions in a finite cylinder. Boll. Un. Mat. Ital. C (6), 3(1):371-391, 1984. |
| [75] | Nicola Garofalo. On a theorem of compact imbedding between Volevic-Panejah spaces. Atti Sem. Mat. Fis. Univ. Modena, 28(1):160-173, 1979. |