Jorge Guillermo Hounie

Professor Titular do Departamento de Matemática da Universidade Federal de São Carlos.
 
 

e-mail:        hounie@dm.ufscar.br                    hounie@power.ufscar.br    Endereço:   Departamento de Matemática                      Universidade Federal de São Carlos                      Rodovia Washington Luiz, km 235                      São Carlos, SP                       CEP: 13565-905

• Nascido em Bahía Blanca, Argentina
• Ph. D. in Mathematics - Rutgers, the State University, 1974
• Professor Titular no DM-UFSCar desde março/1995
• Professor Titular aposentado e Professor Voluntário DM-UFSCar desde maio/2010
  
• Pesquisador do CNPq - Nivel IA
  
• Membro Titular da Academia Brasileira de Ciencias
  

Interesses e Projetos

Existência, regularidade, unicidade e outras propriedades das soluções de Equações Diferenciais Parciais lineares e não lineares.  Teoria Geométrica de Equações Diferenciais Parciais, Operadores Pseudo-Diferenciais, Análise Harmônica, Funções  de Várias Variáveis Complexas.

Projetos:

• Projeto Temático Fapesp "Teoria Geométrica de Equações Diferenciais Parciais e Várias Variáveis Complexas" (Coordenador)
  

• Globally hypoelliptic and globally solvable  first order evolution equations, Trans. Amer. Math. Soc.  252 (1979), 233--248.
• Minimal sets of families of vector fields on  compact surfaces, J. Diff. Geometry 16   (1981)  , 739--744.
• Globally hypoelliptic vector fields on  compact surfaces, Comm. P.D.E. 7 (1982), 343--370.
• Global Cauchy problems modulo flat functions,  Advances in Math. 51 (1984), 240--252.
• On the L^2 continuity of pseudo-differential operators,  Comm. in P.D.E. 11 (1986), 765--778.
• (com A. Bergamasco e P. Cordaro)   Global properties of a class of vector fields in the plane,  J. Diff. Equations 74 (1988), 179--199.
• (com Cordaro)  Local solvability in C_c^¥ of overdetermined systems of vector  fields,   J. Funct. Anal.,  87 (1989), 231--249.
• (com P. Cordaro)  On local solvability of underdetermined systems of vector fields,  Amer. J. Math. 112 (1990), 243--270.
• Local solvability of first order linear operators with Lipschitz coefficients, Duke Math. J. 62 (1991), 467-477.
• The Mizohata structure on the sphere, Trans. Amer. Math. Soc. 334 (1992), 641--649.
• (com J.R. dos Santos Filho) Well posed Cauchy problems for complex nonlinear equations must be semilinear,  Math. Ann. 294 (1992), 439--447.
• (com P. Malagutti) Local integrability of Mizohata structures, Trans. Amer. Math. Soc. 338 (1993), 337--362.
•  (com M. L. Leite)  The maximum principle for hypersurfaces with vanishing curvature functions,  J. Diff. Geometry 41 (1995), 247--258.
• (com P. Santiago)  On local solvability of semilinear equations,   Comm. P. D. E.  20 (1995), 1777--1789.
• (com M. E. Moraes)  Local solvability of first order linear operators with Lipschitz coefficients in two variables, J.  Diff. Equations 121 (1995), 406--416.
• (com J. Álvarez)   Functions of pseudo-differential operators of non-positive order,  J. Funct. Anal. 144  (1996), 45--59.
• (com  J. Tavares)  On removable singularities of locally solvable differential operators,   Inventiones Math.  126 (1996), 589--625.
• (com P. Malagutti)  On the convergence of the  Baouendi-Treves approximation formula,  Comm. P.D.E.   23 (1998), 1305--1347.
• (com M. L. Leite)  Uniqueness and nonexistence theorems for hypersurfaces with H_r=0, Ann. Global  Anal. Geom. 17 (1999),  397--407.
• (com J. Álvarez)   An oscillatory singular integral operator with  polynomial phase, Studia Mathematica 133 (1999),  1--18.
• (com M. L. Leite)  Two-ended hypersurfaces with zero scalar curvature, Indiana Univ. Math. J. 48 (1999), 867--882.
• (com P. Cordaro)   Local solvability for top degree forms in a class of  systems of vector fields,   Amer. J.  Math.  121 (1999), 487--495.
• (com S. Berhanu)   Uniqueness for Locally Integrable Solutions of  Overdetermined Systems,   Duke Math. J., 105 (2000), 387--410.
• (com S. Berhanu e P. Santiago)   A  similarity principle for complex vector fields and applications, Trans. Amer. Math. Soc., 353 (2001), 1661--1675..
• (com S. Berhanu)   An F. and M. Riesz theorem for planar vector fields,  Math. Ann., 320, (2001), 463-485.
• (com P. Cordaro) Local solvability for a class of differential complexes, Acta Math., 187:2, (2001), 191-212..
• (com S. Berhanu)  On  boundary properties of solutions of complex vector fields,   J. Funct. Anal.,  192, (2002), 446--490.
• (com E. da Silva)  A  Similarity Principle for Locally  Solvable Vector Fields,  J. Math. Pures Appl.,  81,  (2002), 715--746.
• (com S. Berhanu)  Traces and the F. and M. Riesz theorem for  vector fields, Ann. Inst. Fourier,  53, (2003), 1425--1460.
• (com S. Berhanu)  On boundary regularity for one-sided locally solvable vector fields, Indiana Univ. Math. J., 52, (2003), 1447--1477.
• (com L. A. Carvalho dos Santos)  Estimates for the Poisson kernel and Hardy spaces on compact manifolds,   J. of Math. An. and Appl., 299 (2004), 465--493.
• (com S. Berhanu)  The F. and M. Riesz property for vector fields,  Contemporary Math. 368, (2005), 25--39.
• (com F. Brito e M. L. Leite) Liouville's formula in arbitrary planar domains,  Nonlinear Analysis, 60, (2005), 1287--1302.
• (com S. Berhanu)  An F. and M. Riesz theorem for a system of vector fields,   Inventiones Math., 162, (2005), 357--380.
• (com E. Lanconelli)  An Alexandrov  type theorem for Reinhardt domains of  C², Contemporary Math., 400, (2006), 129--146.
• (com S. Berhanu)  On the F. and M. Riesz theorem on wedges with edges of class C^1,alpha ,  Mathematische Zeitschift 255, (2007), 161--175.
• (com G. Hoepfner)   Locally solvable vector fields and Hardy spaces, J. Funct. Anal. 247, (2007), 378--416.
• (com E. Lanconelli)  A sphere theorem for a class of Reinhardt domains with constant Levi curvature. Forum Mathematicum,  20, (2008),  571--586.
  
• . A proof of Bochner's tube theorem. Proceedings of the American Mathematical Society, 137, ( 2009), 4203--4207.
• (com R. Kapp)   Pseudodifferential operators on local Hardy spaces. Journal of Fourier Analysis and Applications, 15,  (2009), 153--178.
• (com S. Berhanu)  A Rudin-Carleson theorem for planar vector fields. Mathematische Annalen, 347, (2010), 65--110.
• (com T. Picon)  Local Gagliardo-Nirenberg estimates for elliptic systems of vector fields. Mathematical Research Letters, (2011), 18,  791--804.
  
• (com S. Berhanu)  A generalization of Bochner's extension theorem to rough tubes. The Journal of Geometric Analysis, 21, (2011), 455--475.
  
• (com G. Hoepfner e L. A. C. dos Santos)  Tube structures, Hardy spaces and extension of CR distributions. Transactions of the American Mathematical Society,  363, (2011), 5091--5109.
• (com S. Berhanu)  A class of FBI transforms. Communications in Partial Differential Equations, 37, (2012) ,38--57.
  
• (com G. Hoepfner e L. A. C. dos Santos)  On the Extension of h^p-CR distributions defined on rough tubes. Proceedings of the American Mathematical Society, 140, (2012),627--633.
  
• (com S. Berhanu)  Boundary behavior of generalized analytic functions. Journal of Functional Analysis, 266, (2014), 4121--4149.
  
• (com S. Berhanu)  On vector fields in the plane with the reflection property. Transactions of the American Mathematical Society, 366, (2014), 1703--1723.
• (com G. Hoepfner e T, Picon)  Div-curl type estimates for elliptic systems of complex vector fields. Journal of Mathematical Analysis and Applications , v429, (2015), 774--799.
• (com T. Picon)  Local L¹ estimates for elliptic systems of complex vector fields. Proceedings of the American Mathematical Society, 143, (2015) , 1501--1514.