# Complex Variables and Elliptic Equations

Publisher: Taylor & Francis

## Description

• Impact factor
0.50
• 5-year impact
0.00
• Cited half-life
4.00
• Immediacy index
0.07
• Eigenfactor
0.00
• Article influence
0.00
• Other titles
Complex variables and elliptic equations (Online), Complex variables
• ISSN
1747-6933
• OCLC
63766506
• Material type
Document, Periodical, Internet resource
• Document type
Internet Resource, Computer File, Journal / Magazine / Newspaper

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author cannot archive a post-print version
• Restrictions
• 12 month embargo for STM, Behavioural Science and Public Health Journals
• 18 month embargo for SSH journals
• Conditions
• Some individual journals may have policies prohibiting pre-print archiving
• Pre-print on authors own website, Institutional or Subject Repository
• Post-print on authors own website, Institutional or Subject Repository
• Publisher's version/PDF cannot be used
• On a non-profit server
• Published source must be acknowledged
• Must link to publisher version
• Set statements to accompany deposits (see policy)
• Publisher will deposit to PMC on behalf of NIH authors.
• STM: Science, Technology and Medicine
• SSH: Social Science and Humanities
• 'Taylor & Francis (Psychology Press)' is an imprint of 'Taylor & Francis'
• Classification
​ yellow

## Publications in this journal

• ##### Article: Local homeomorphisms satisfying generalized modular inequalities
[hide abstract]
ABSTRACT: We study the geometric properties of the local homeomorphisms satisfying some generalized modular inequalities. We establish in Theorem 1 that a local homeomorphism f:D included in Rn →Rn satisfying condition (N) and having local ACLq inverses, with q>1, satisfy important modular inequalities. We generalize in this class of mappings known theorems from the theory of quasiregular mappings like Zoric’s theorem and the estimate of the radius of injectivity.
Complex Variables and Elliptic Equations 12/2013;
• ##### Article: Left Cauchy–Riemann operator and Dolbeault–Grothendieck lemma on the group of Heisenberg type . n (C)
[hide abstract]
ABSTRACT: We extend to differential forms the system of partial differential equations ∂l Hu = f defined for functions as follows ⎧⎪⎪⎪⎨ ⎪⎪⎪⎩ ∂u ∂z j + i 4 k=�n−m k=1 � ∂ Bk ∂z j ∂u ∂ζk + ∂ Bk ∂z j ∂u ∂ζ k � = f j 1 ≤ j ≤ m, ∂u ∂ζ k = fm+k 1 ≤ k ≤ n − m. This leads to the ∂l H −cohomology, and then we will prove the corresponding Dolbeault–Grothendieck lemma
Complex Variables and Elliptic Equations 09/2013; 58(9).
• Source
##### Article: On separately subharmonic and harmonic functions
[hide abstract]
ABSTRACT: We improve our previous generalizations to Arsove's and Ko\lodziej's and Thorbi\"ornson's results concerning the subharmonicity of a function subharmonic with respect to the first variable and harmonic with respect to the second.
Complex Variables and Elliptic Equations 09/2013; 59 (2014)(2):149-161.
• ##### Article: On the solutions of generalized Cauchy–Riemann system
[hide abstract]
ABSTRACT: The paper, mainly deals with the question of existence of the solutions of the generalized Cauchy–Riemann system in function spaces, in particular, in the space of bounded analytic functions. Without summability assumption on the coefficients of the equation, existence of the solutions for the whole complex plane is proved
Complex Variables and Elliptic Equations 09/2013;
• ##### Article: On existence and representation of solutions for general degenerate Beltrami equations
[hide abstract]
ABSTRACT: We study the Dirichlet problem for general degenerate Beltrami equation ${\overline {\partial}}f\, =\, \mu {\partial f}+\nu {\overline {\partial f}}$ in the unit disk D in C. Given an arbitrary analytic function A with isolated singularities in D, we find criteria for the existence of a solution f of the form f = A◦ω where ω stands for a regular W1,1loc (D) himeomorphism of D onto itself. Some criteria for the existence of regular solutions are given.
Complex Variables and Elliptic Equations 01/2013;
• ##### Article: A Finite Class of Orthogonal Functions Generated by Routh-Romanovski Polynomials
[hide abstract]
ABSTRACT: It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh–Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity.
Complex Variables and Elliptic Equations 09/2012; 59(2):162-171.
• ##### Article: Commutator of composition operators with adjoints of composition operators
[hide abstract]
ABSTRACT: We characterize the compactness of the linear fractionally induced commutator in terms of the function theoretic properties of and ψ. We show that in the automorphic case the commutator is compact if and only if and ψ are simple rotations of the unit disc. On the other hand, when one of the inducing maps is not an automorphism of the disc, we show that the commutator is non-trivially compact if and only if the inducing maps are both parabolic with the same boundary fixed point or they are both hyperbolic with the same boundary fixed point and their other fixed points are conjugate reciprocals.
Complex Variables and Elliptic Equations 06/2012; 57(6):677-686.
• ##### Article: Peak points and peaking functions for P(K)
[hide abstract]
ABSTRACT: Let K   be compact and \K connected, P(K) the uniform closure of all polynomial functions restricted to K and A(K) the uniform algebra of all functions continuous on K and holomorphic on int(K). It is known (Mergelyan) that P(K) = A(K) if and only if \K is connected. Let ∂K be the topological boundary of K and (P(K)) = {z  K: there exists f  P(K) such that f (z) = 1, |f(w)| < 1 for w  K\{z}}, i.e., the set of peak points relative to P(K). A long standing problem is to determine the family of K's such that (P(K)) = ∂K. We give new results for the solution to this problem by using two different methods. The first one uses no notions of capacity and only employs results from classic complex variable theory and topology. We prove that for every K, there is a dense subset of ∂K (‘escape’ points) contained in (P(K)) such that each escape point has a peaking function, that is a homeomorphism on K and is conformal on int(K). The second uses the Curtis Peak Point Criterion which depends on properties of capacity. From this, we prove not only that (P(K))  ∂K (long known), but finally that (P(K)) = ∂K for all K.
Complex Variables and Elliptic Equations 06/2012; 57(6):611-624.
• ##### Article: On approximation in weighted Smirnov–Orlicz classes
[hide abstract]
ABSTRACT: In this work, we investigate the approximation problems in weighted Smirnov–Orlicz classes. We prove a direct theorem for polynomial approximation of functions in certain subclasses of weighted Smirnov–Orlicz classes. The direct theorem is proved in terms of the modulus of smoothness. Also, from the main theorem some results are obtained. In the proof of the main theorem, a Jackson-Dzjadyk polynomial is used.
Complex Variables and Elliptic Equations 05/2012; 57(5):567-577.
• ##### Article: Local smoothing effect and existence for the one-phase Hele–Shaw problem with zero surface tension
[hide abstract]
ABSTRACT: We study an initial value problem for the one-phase Hele–Shaw problem with zero surface tension. We establish local well-posedness for the initial value problem in Sobolev space. Furthermore, we obtain that, on average in time, the solution gains 1/2 derivative of smoothness in spatial variable compared to the initial data.
Complex Variables and Elliptic Equations 02/2012; 57(Nos. 2–4):351-368.
• ##### Article: Heat kernels for a class of degenerate elliptic operators using stochastic method
[hide abstract]
ABSTRACT: Formulas for heat kernels are found for degenerate elliptic operators by finding the probability density of the associated Ito diffusion. The formulas involve an integral of a product between a volume function and an exponential term.
Complex Variables and Elliptic Equations 02/2012; 57(Nos. 2–4):155-168.
• ##### Article: Variational approach to noncoercive systems of elliptic variational inequalities via trapping region†
[hide abstract]
ABSTRACT: This article deals with a system of quasilinear elliptic variational inequalities whose leading differential operator is a diagonal (p 1, p 2)-Laplace operator with 1 < p 1, p 2 < ∞, and whose lower order vector field f = (f 1, f 2) is a gradient field, which is not subject to any growth restriction, in particular, it may have supercritical growth, and thus coercivity is violated. The novelty of this article is to establish a variational approach of the, in general, noncoercive elliptic system of variational inequalities by introducing the concept of trapping region for such type of problems. The trapping region allows us to transform the given noncoercive system of variational inequalities into an associated ‘truncated’ system to which variational methods can be applied. We are going to prove that the ‘truncated’ system possesses solutions, which can be characterized as the critical points of a suitably constructed (nonsmooth) energy functional, and any critical point is shown to be a solution of the original problem within the trapping region. Moreover, applications to quasilinear elliptic systems under Dirichlet boundary conditions as well as to elliptic systems under obstacle constraints are treated by the theory developed in this article.
Complex Variables and Elliptic Equations 02/2012; 57(Nos. 2–4):169-183.
• ##### Article: Power matrices for Faber polynomials and conformal welding
[hide abstract]
ABSTRACT: The power matrix is the matrix of the coefficients of the power series at 0 of powers of an analytic function. Composition corresponds to matrix multiplication. We generalize the power matrix by replacing power series with Faber polynomial expansions. We show that composition corresponds to multiplication of the generalized power matrices, for both simply and doubly connected domains. We apply this to give some matrix product formulas for the coefficients of conformal welding maps of an analytic homeomorphism of an analytic curve. In particular, in some sense one can solve for the coefficients of the conformal welding maps in terms of the generalized power matrix of the analytic homeomorphism.
Complex Variables and Elliptic Equations 01/2012;
• ##### Article: Infinite type germs of real analytic pseudoconvex domains in ℂ
[hide abstract]
ABSTRACT: In Lampert [On the boundary regularity of biholomorphic mappings, Contributions to several complex variables, Aspects Math. E9 (1986), pp. 193–215] and D'Angelo [Several Complex Variables and the Geometry of real Hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993, ISBN: 0-8493-8272-6] Lempert and D'Angelo showed that germs of real analytic sets in ℂ of infinite type contain a complex curve. In this article we discuss a very special case of their result, germs of real analytic pseudoconvex domains in ℂ. We reprove their theorem using a geometric construction which sheds light on the intricate structure of such boundaries in the presence of complex curves of high order tangency. The proof of Lempert and D'Angelo is somewhat more of an ideal theoretic nature.
Complex Variables and Elliptic Equations 01/2012; 57(6):705-717.
• Source
##### Article: The Carathéodory and Kobayashi/Royden metrics by way of dual extremal problems
[hide abstract]
ABSTRACT: We study the Carathéodory and Kobayashi metrics by way of the method of dual extremal problems in functional analysis. Particularly, incisive results are obtained for convex domains.
Complex Variables and Elliptic Equations 01/2012;

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