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Pubblicazioni antecedenti il 2004
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[1] B. Franchi, Spazi di Banach e forme quadratiche quasi non
singolari, Boll. Un. Mat Ital. 10 (1974), 440-450.
[2] B. Franchi, Su un teorema di R.H. Martin jr., Rend. Sem. Mat.
Univ. Padova 55 (1976), 275-288.
[3] A. Bove, B. Franchi & E. Obrecht, An Initial-Boundary Value
Problem with Mixed Lateral Conditions for Heat Equation, Ann. Mat.
Pura Appl. (4) 121, 277-307.
[4] A. Bove, B. Franchi & E. Obrecht, Elliptic Equations with
Polynomially Growing Coefficients in a Half Space, Boll. Un. Mat.
Ital. 17-B (1980), 823-834.
[5] A. Bove, B. Franchi & E. Obrecht, A Boundary Value Problem
for Elliptic Equations with Polynomial Coefficients in a Half Space
I: Pseudodifferential Operators and Function Spaces, Boll. Un. Mat.
Ital. 18-B (1980), 25-45.
[6] A. Bove, B. Franchi & E. Obrecht, A Boundary Value Problem
for Elliiptic Equations with Polynomial Coefficients in a Half
Space II: The Boundary Value Problem, Boll. Un. Mat. Ital. 18-B
(1980), 355-380.
[6a] A. Bove, B. Franchi & E. Obrecht, An Elliptic Boundary
Value Problem with Unbounded Coefficients in a Half Space, Atti
Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (8) 65 (1978),
265-268.
[7] A. Bove, B. Franchi & E. Obrecht, Boundary Value Problems
for Operators like ∆ + x ∇, Rend. Mat. (7) 1 (1981), 95-120.
[7a] A. Bove, B. Franchi & E. Obrecht, Elliptic Equations
Containing the Term r∂ r in a Half Space, Atti Accad. Naz. Lincei
Cl. Sci. Fis. Mat. Natur. (8) 67 (1979), 223-226.
[8] A. Bove, B. Franchi & E. Obrecht, Parabolic Problems with
Mixed Time Dependent Lateral Conditions, Comm. Partial Differential
Equations 7 (1982), 1253-1288.
[9] A. Bove, B. Franchi & E. Obrecht, Parabolic Problems in
Weighted Sobolev Spaces, Ricerche Mat. 31 (1982), 45-68.
[10] A. Bove, B. Franchi & E. Obrecht, Boundary Value Problems
with Mixed Lateral Conditions for Parabolic Operators, Ann. Mat.
Pura Appl. (4) 131 (1982), 375-413.
[10a] A. Bove, B. Franchi & E. Obrecht, Problèmes aux limites
avec des conditions laterales de type melé pour des opérateurs
paraboliques, Seminaire d'Analyse, Université de Nantes
(1980/81).
[11] A. Bove, B. Franchi & E. Obrecht, Straightening of a
Noncylindrical Region and Evolution Equations, Rend. Sem. Mat.
Univ. Padova 71 (1984), 207-216.
[12] B. Franchi, E. Lanconelli, Une métrique associée à une classe
d'opérateurs elliptiques dégénerés, Rend. Sem. Mat. Univ. e
Politec. Torino, Proceedings of the meeting "Linear Partial and
Pseudo Differential Operators", Fascicolo Speciale (1982).
[13] B. Franchi, E. Lanconelli, An Embedding Theorem for Sobolev
Spaces Related to Non- Smooth Vector Fields and Harnack Inequality,
Comm. Partial Differential Equations 9 (1984), 1237-1264.
[14] B. Franchi, E. Lanconelli, Hoelder regularity Theorem for a
Class of Linear Non Uniformly Elliptic Operators with Measurable
Coefficients, Ann. Scuola Norm. Sup. Pisa (4) 10 (1983), 523-541.
[14a] B. Franchi, E. Lanconelli, De Giorgi's Theorem for a Class of
Strongly Degenerate Elliptic Equations, Atti Accad. Naz. Lincei,
Cl. Sci. Fis. Mat. Natur. (8) 72 (1982), 273-277.
[15] B. Franchi, Trace Theorems for Anisotropic Weighted Sobolev
Spaces in a Corner, Math. Nachr. 127 (1986), 25-50.
[16] B. Franchi, Proprietés des courbes intégrales de champs de
vecteurs et estimations ponc- tuelles d'equations elliptiques
dégénérées, séminaire Goulaouic-Meyer-Schwartz 1983-1984, Exposé n.
3.
[17] B. Franchi, E. Lanconelli, Une condition geometrique pour
l'inegalité de Harnack, J. Math. Pures Appl. 64 (1985), 237-256.
[18] B. Franchi, E. Lanconelli & J. Serrin, Existence and
Uniqueness of Ground States Solu- tions of Quasilinear El liptic
Equations, Nonlinear Diffusion Equations and their Equilibrium
States, Springer, 1988.
[18a] B. Franchi, E. Lanconelli & J. Serrin, Esistenza e
unicità degli stati fondamentali per e- quazioni el littiche
quasilineari, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur.
(8) 79 (1985), 212-216.
[19] B. Franchi, E. Lanconelli, Radial Symmetry of the Ground
States for a Class of Quasilinear El liptic Equations, Nonlinear
Diffusion Equations and their Equilibrium States, Berkeley 1986,
Springer, 1988.
[20] B. Franchi, R. Serapioni, Pointwise Estimates for a Class of
Strongly Degenerate Elliptic Operators: a Geometrical Approach,
Ann. Scuola Norm. Sup. Pisa (4) 14 (1987), 527-568.
[21] B. Franchi, Weighted Sobolev-Poincaré Inequalities and
Pointwise Estimates for a Class of Degenerate Elliptic Equations,
Trans. Amer. Math. Soc. 327 (1991), 125-158.
[22] B. Franchi, Global Solutions for a Class of Monge-Ampère
Equations, Nonlinear Diffusion Equations and their Equilibrium
States II, Gregynog 1989, Birkhauser, 1992.
[23] M. Bertsch, R. Dal Passo & B. Franchi, A degenerate
Parabolic Equation in Noncylindrical Domains, Math. Ann. 294
(1992), 551-587.
[24] B. Franchi, Inégalités de Sobolev pour des champs de vecteurs
lipschitziens, C. R. Acad. Sci. Paris, Ser. A 311 (1990),
329-332.
[25] B. Franchi, N. Kutev & S. Polidoro, Nontrivial Solutions
for Monge-Ampère Type Operators in Convex Domains, Manuscripta
Math. 79 (1993), 13-26.
[26] B. Franchi, F. Serra Cassano, Régularité partielle pour une
classe de systèmes elliptiques dégénérés, C. R. Acad. Sci. Paris,
Ser. A 316 (1993), 37-40.
[27] B. Franchi, C. Gutierrez & R.L. Wheeden, Weighted
Sobolev-Poincaré inequalities for Grushin type operators, Comm.
Partial Differential Equations 19 (1994), 523-604.
[28] B. Franchi, S. Gallot & R.L. Wheeden, Sobolev and
isoperimetric inequalities for degenerate metrics, Math. Ann. 300
(1994), 557-571.
[28a] B. Franchi, S. Gallot & R.L. Wheeden, Inégalités
isopérimetriques pour des métriques dégénérées, C. R. Acad. Sci.
Paris, Ser. A 317 (1993).
[29] B. Franchi, E. Lanconelli & J. Serrin, Existence and
uniqueness of Nonnegative Solutions of Qualinear Elliptic Equations
in Rn , Advances in Math. 118 (1996), 177-243. [30] B. Franchi, F.
Serra Cassano, Gehring's lemma for metrics and higher integrability
of the gradient for minimizers of noncoercive variational
functionals, Studia Math. 120 (1996), 1-22.
[31] B. Franchi, C. Gutierrez & R.L. Wheeden, Two-weight
Sobolev-Poincaré inequalities and Harnack inequality for a class of
degenerate el liptic operators, Atti Accad. Naz. Lincei, Cl. Sci.
Fis. Mat. Natur. (9), 5 (1994), 167-175.
[32] J.C Fernanes, B. Franchi, Existence and properties of the
Green function for a class of degenerate parabolic equations, Rev.
Mat. Iberoamericana 12 (1996), 491-525.
[33] C. Cancelier, B. Franchi, Subelliptic estimates for a class of
degenerate elliptic integr- differential operators, Math. Nachr.
183 (1997), 19-41.
[34] B. Franchi, G. Lu & R.L. Wheeden, Representation formulas
and weighted Poincaré in- equalities for Hormander vector
fields, Ann. Inst. Fourier 45 (1995), 577-604. [35] B.
Franchi, G. Lu & R.L. Wheeden, Weighted Poincaré inequalities
for Hormander vector fields and local regularity for a
class of degenerate el liptic equations, Potential Analysis 4
(1995), 361-375.
[36] B. Franchi, G. Lu & R.L. Wheeden, A relationship between
Poincaré type inequalities and representation formulas in metric
spaces, Int. Math. Res. Not. (1996), 1-14.
[37] B. Franchi, R. Serapioni & F. Serra Cassano, Meyers-Serrin
type theorems and relaxation of variational integrals depending on
vector fields, Houston Math. J. 22 (1996), 859-889..
[37a] B. Franchi, R. Serapioni & F. Serra Cassano, Champs de
vecteurs, théorème d'approximation de Meyers-Serrin et phenomène de
Lavrentev pour des fonctionel les dégénérées, C. R. Acad. Sci.
Paris 320 (1995), 695-698.
[38] B. Franchi, R. Serapioni & F. Serra Cassano, Approximation
and imbedding theorems for weighted Sobolev spaces associated with
Lipschitz continuous vector fields, Boll. Un. Mat. Ital. (7) 11-B
(1997), 83-117.
[39] B. Franchi, R.L. Wheeden, Compensation couples and
isoperimetric estimates for vector fields, Colloquium Math. 74
(1997), 9-27.
[40] B. Franchi, M.C. Tesi, A finite element
approximation for a class of degenerate el liptic equations, Math.
Comput. 69 (2000), 41-63.
[41] B. Franchi, R. Serapioni & F. Serra Cassano, Discontinuous
solutions of linear degenerate el liptic equations, Potential Anal.
9 (1998), 201-216.
[42] B. Franchi, L.A. Peletier, Ground states for Gaussian
curvature type equations, Asymptotic Analysis 17 (1998),
53-70.
[43] B. Franchi, R.L. Wheeden, Some remarks about Poincaré type
inequalities and representa- tion formulas in metric spaces of
homogeneous type, J. Inequal. Appl. 3 (1999), 65-89.
[44] B. Franchi, C. Pérez & R.L. Wheeden, Self-Improving
Properties of John-Nirenberg and Poincaré Inequalities on Spaces of
Homogeneous Type, J. Funct. Analysis 153 (1998), 108- 146.
[45] B. Franchi, P. Hajlasz & P. Koskela, On
definitions of Sobolev classes on metric spaces, Ann.
Inst. Fourier (Grenoble) 49 (1999), 1903-1924.
[46] B. Franchi, C. Pérez & R.L. Wheeden, Sharp geometric
Poincaré inequalities for vector fields and non-doubling
measures, Proc. Lond. Math. Soc. (3) 80 (2000), 665-689.
[47] C. Cancelier, B. Franchi & E. Serra, Agmon distance for
sum-of-squares operators, J. Anal- yse Math. 83 (2001),
89-107.
[48] A. Baldi, B. Franchi & M.C. Tesi, Uniform error estimates
and a finite element approxi- mation for degenerate
elliptic equations, Le Matematiche 54, Suppl. (1999), 49-60.
[49] B. Franchi, P. Hajlasz, How to get rid of one of the weights
in a two weight Poincaré inequality?, Ann. Pol. Math. 74 (2000),
97-103.
[50] B. Franchi, R. Serapioni, F. Serra Cassano,
Rectifiability and perimeter in the Heisenberg group,
Math. Ann. 321 (2001), 479-531.
[50a] B. Franchi, R. Serapioni, F. Serra Cassano, Sur les ensembles
rectifiables dans le groupe de Heisenberg, C. R. Acad.
Sci., Paris, Ser. I, Math. 329 (1999), 183-188. [51] B. Franchi,
M.C. Tesi, Homogenization for strongly anisotropic nonlinear
elliptic equations, NoDEA 8 (2001), 363-387.
[52] F. Ferrari, B. Franchi, A local doubling formula for the
harmonic measure associated with subelliptic operators and
applications, Comm. Partial Differential Equations 28 (2003), 1-60.
[53] F. Ferrari, B. Franchi, Geometry of the boundary and doubling
property of the harmonic measure for Grushin type operators,
Proceedings of the meeting "Partial Differential Oper- ators"
(Torino, 2000), Rend. Sem. Mat. Univ. Politec. Torino 58 (2002),
281-299.
[54] A. Baldi, B. Franchi & G. Lu, An existence result for
degenerate elliptic pde's, Ricerche Mat., special issue in honor of
E. De Giorgi 49, suppl. (2000), 177-193.
[55] B. Franchi, M.C. Tesi, Two-scale homogenization in the
Heisenberg group, J. Math. Pures Appl. (9) 81 (2002), 495-532.
[56] A. Baldi, B. Franchi, A Γ-convergence result for doubling
metric measures and associated perimeters, Calc. Var. Partial
Differential Equations, 16 (2003), 283-298.
[57] B. Franchi, R. Serapioni, F. Serra Cassano, Regular
hypersurfaces, intrinsic perimeter and implicit function theorem in
Carnot groups, Comm. Anal. Geom. 11 (2003), 909-944. [58] B.
Franchi, R. Serapioni, F. Serra Cassano, On the structure of
finite perimeter sets in step 2 Carnot groups, J. Geom.
Anal. 13 (2003), 421-466.
[58a] B. Franchi, R. Serapioni, F. Serra Cassano,
Rectifiability and perimeter in step 2 Groups, in
"Proceedings of Equadiff10, Prague Aug. 2001", Math. Bohem. 127
(2002), 219-228.
[59] B. Franchi, C. Pérez & R.L. Wheeden, A sum operator with
applications to self-improving properties of Poincaré inequalities
in metric spaces, J. Fourier Anal. Appl. 9 (2003), 511- 540.
[60] B. Franchi, BV spaces and rectifiability for
Carnot-Carathéodory metrics: an introduction, Proceedings of
NAFSA7, Prague July 2002, Acad. Sci. Czech Rep., Olympia Press,
2004.
[61] F. Ferrari, B. Franchi & G. Lu, On a relative
Alexandrov-Fenchel inequality for convex bodies in Euclidean
spaces, Forum Math. 18 (2006), 907-921.
[61] Y. Achdou, B. Franchi & N. Tchou, A partial differential
equation connected to option pricing with stochastic volatility:
regularity results and discretization, Math. Comp. 74 (2005),
1291-1322.
[62] A. Baldi, B. Franchi, Mumford-Shah type functionals associated
with doubling metric measures, Proc. Roy. Soc. Edinburgh Sec A 135
(2005), 1-23.
[63] F. Ferrari, B. Franchi & H. Pajot, The geometric traveling
salesman problem in the Heisen- berg group, Rev. Mat.
Iberoamericana 23 (2007), 437-480.
[63a] F. Ferrari, B. Franchi & H. Pa jot, Courbure et
sous-ensembles de courbes rectifiable dans le group de Heisenberg,
Séminaire d' Equations aux Dérivées Partielles. 2005-2006, Exp. No.
XII, 12 pp., Ecole Polytech., Palaiseau. (2006).
[64] B. Franchi, R. Serapioni & F. Serra Cassano, Regular
submanifolds, graphs and area formula in Heisenberg groups, Adv.
Math. 211 (2007), 152-203.
[65] B. Franchi, C.E. Gutierrez & Truyen Van Nguyen,
Homogenization and convergence of correctors in Carnot groups,
Comm. Partial Differential Equations 30 (2005), 1817-1841.
[66] B. Franchi, N. Tchou & M.C. Tesi, div-curl type Theorem,
H-convergence, and Stokes for- mula in the Heisenberg group, Comm.
Comtemp. Math. 8 (2006), 67-99.
[67] B. Franchi, E. Serra, Convergence of a class of degenerate
Ginzburg-Landau functionals and regularity for a subelliptic
harmonic map equation, J. Analyse Math. 100 (2006), 281-322.
[67a] B. Franchi, E. Serra, Degenerate Ginzburg-Landau functionals,
J. Nonlinear Convex Anal. 7 (2006), 443-452.
[68] A. Baldi, B. Franchi & M.C. Tesi, Fundamental solution
and sharp Lp estimates for Laplace operators in the contact complex
of Heisenberg groups, Ricerche Mat. 1 (2006), 119-144.
[69] A. Baldi, B. Franchi & M.C. Tesi, Compensated
compactness in the contact complex of Heisenberg groups, Indiana
Univ. Math. J. 81 (2008), 133-186.
[69a] A. Baldi, B. Franchi & M.C. Tesi, Compensated
compactness, div-curl theorem and H- convergence in general
Heisenberg groups, proceedings of the meeting "Subelliptic pde's
and applications to geometry and finnance" (Cortona 12-17 giugno
2006), Lect. Notes Semin. Interdiscip. Mat. Dep. Mat. Univ.
Basilicata, Potenza 6 (2006), 33-47.
[70] B. Franchi, R. Serapioni & F. Serra Cassano, Intrinsic
Lipschitz graphs in Heisenberg groups, J. Nonlinear Convex Anal. 7
(2006), 423-441.
[71] B. Franchi, R. Serapioni & F. Serra Cassano, Intrinsic
submanifolds, graphs and currents in Heisenberg groups, proceedings
of the meeting "CR Geometry and PDEs" (Levico Terme, 12-16
settembre 2004), Lect. Notes Semin. Interdiscip. Mat. Dep. Mat.
Univ. Basilicata, Potenza 4 (2005), 23-38.
[72] A. Baldi, B. Franchi & M.C. Tesi, Hypoellipticity,
fundamental solution and Liouville type theorem for matrix-valued
differential operators in Carnot groups, J. Eur. Math. Soc., 11
(2009), 777-798.
[73] B. Franchi, R. Serapioni & F. Serra Cassano,
Differentiability of intrinsic Lipschitz functions within
Heisenberg groups, J. Geom. Anal., to appear.
[74] A. Baldi, B. Franchi & M.C. Tesi, Differential forms,
Maxwell equations and compensated compactness in Carnot groups,
proceedings of the meeting ``Geometric Methods in PDE's'' (Bologna,
27--30 maggio 2008), Lect. Notes Semin. Interdiscip. Mat. Dep. Mat.
Univ. Basilicata, Potenza 7 (2008), 21--40.
[75] A. Baldi, B. Franchi, N. Tchou & M.C. Tesi,
Compensated compactness for differential forms in Carnot groups and
applications, Adv. Math. 223(2010), 1555--1607
[76] B. Franchi & M.C. Tesi, Faraday's form and Maxwell's
equations in the Heisenberg group, Milan J. Math. 77 (2009),
245--270.
[77] F. Ferrari, B. Franchi, & I. Verbitsky, Hessian
inequalities and the fractional Laplacian, J. Reine Angew. Math.,
to appear.
[78] B. Franchi & M.C. Tesi, Wave and Maxwell's
Equations in Carnot Groups, Comm. Comtemp. Math., to appear.
[79] A. Baldi & B. Franchi, Differential forms in
Carnot groups: a $\Gamma$-convergence approach, Calc. Var. Partial
Differential Equations, to appear.
[80] Y. Achdou, B. Franchi, N. Marcello & M.C. Tesi, A
Qualitative Model for Diffusion and Aggregation of $\beta$-Amyloid
in Alzheimer's disease, preprint (2011)
