|
A similarity principle for complex vector fields and applications
Author(s):
S.
Berhanu;
J.
Hounie;
P.
Santiago
Journal:
Trans. Amer. Math. Soc.
353
(2001),
1661-1675.
MSC (1991):
Primary 35F05, 35N10, 35A05;
Secondary 35F20, 32F40
Posted:
November 29, 2000
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
This paper establishes a similarity principle for a class of non-elliptic, smooth complex vector fields in the plane. This principle is used to prove a uniqueness result for a nonlinear Cauchy problem.
References:
-
- 1.
- J. Alvarez and J. Hounie, Estimates for the kernel and continuity properties of pseudo-differential operators. Arkiv för Mat. 28 (1990), 1-22.
- 2.
- L. Bers, An outline of the theory of pseudoanalytic functions. Bull. Amer. Math. Soc. 62 (1956), 291-331. MR 18:470d
- 3.
- L. Bers, Theory of pseudo-analytic functions. Institute for Math. and Mech., New York Univ., New York, (1953). MR 15:211c
- 4.
- L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Convegno Internationale sulle Equazioni Lineari alle Derivate Parziali, Edition Cremonese(Rome), (1955), 111-140. MR 17:974d
- 5.
- D. Colton, Analytic theory of partial differential equations. Pitman(London), (1980). MR 82j:35001
- 6.
- D. Goldberg, A local version of real Hardy spaces. Duke Math. J. 46 (1979), 27-42. MR 80h:46052
- 7.
- J. Hounie, Global Cauchy problems modulo flat functions. Advances in Math. 51 (1984), 240-252. MR 86c:35158
- 8.
- J. Hounie and E. Perdigão, On local solvability in
 of first-order linear operators. J. of Math. Ann. Appl. 197 (1996), 42-53. MR 96j:35005 - 9.
- A. Meziani, On the similarity principle for planar vector fields. Application to Second Order PDE. J. Diff. Equations 157 (1999), 1-19. CMP 2000:01
- 10.
- L. Nirenberg and F. Treves, Solvability of a first order linear partial differential equation. Comm. Pure Appl. Math. 16 (1963), 331-351. MR 29:348
- 11.
- H. Renelt, Elliptic systems and quasiconformal mappings. Pure and Applied Mathematics, Wiley-Interscience, (1988). MR 90k:35086
- 12.
- E. M. Stein, Singular integrals and differentiability properties of functions. Princeton Univ. Press, (1970). MR 44:7280
- 13.
- E. M. Stein, Harmonic Analysis: Real-variable methods, orthogonality, and oscillatory integrals. Princeton Univ. Press, (1993). MR 95c:42002
- 14.
- E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables I. Acta Math. 103 (1960), 25-62. MR 22:12315
- 15.
- F. Treves, Hypoanalytic Structures: Local Theory. Princeton Univ. Press, (1992). MR 94e:35014
- 16.
- I. V. Vekua, Generalized Analytic Functions, Pergamon Press, Oxford, (1962). MR 27:321
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
35F05, 35N10, 35A05,
35F20, 32F40
Retrieve articles in all Journals with MSC
(1991):
35F05, 35N10, 35A05,
35F20, 32F40
Additional Information:
S.
Berhanu
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-6094
Email:
berhanu@euclid.math.temple.edu
J.
Hounie
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, CEP 13.565-905, São Carlos, SP, Brasil
Email:
hounie@dm.ufscar.br
P.
Santiago
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-6094
Address at time of publication:
Departamento de Matemática, Universidade Federal de Pernambuco, CEP 50.740-540, Recife, PE, Brasil
Email:
santiago@dmat.ufpe.br
DOI:
10.1090/S0002-9947-00-02673-8
PII:
S 0002-9947(00)02673-8
Keywords:
Similarity principle,
locally solvable vector field
Received by editor(s):
October 14, 1998
Received by editor(s) in revised form:
October 25, 1999.
Posted:
November 29, 2000
Additional Notes:
The first author thanks IMPA of Brazil for an invitation to a pde workshop in July, 1997, that facilitated this work
The second author was partially supported by CNPq, FAPESP and FINEP
The third author was supported partially supported by CNPq
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org