On the well-posedness of global fully nonlinear first order elliptic systems [PDF]
Advances in Nonlinear Analysis, 2018 In the very recent paper [15], the second author proved that for any f∈L2(ℝn,ℝN){f\in L^{2}(\mathbb{R}^{n},\mathbb{R}^{N})}, the fully nonlinear first order system F(⋅,Du)=f{F(\,\cdot\,,\mathrm{D}u)=f} is well posed in the so-called J. L.
Abugirda Hussien, Katzourakis Nikos
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Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2
Open Mathematics, 2021 By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min +3 more
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Journal of Mathematics, 2021 In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂℂ2 of the complex matrix algebra M4,ℂ. We exhibit regular functions defined on a domain in ℂ4 but taking values in ℂℂ2.
Ji Eun Kim
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A criterion of univalence in Cⁿ in terms of the Schwarzian derivative [PDF]
, 2022 Using the Loewner Chain Theory, we obtain a new criterion of uni- valence in Cⁿ in terms of the Schwarzian derivative for locally biholomorphic mappings. We as well derive explicitly the formula of this Schwarzian derivative using the numerical method of
HERNÁNDEZ, Rodrigo
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Application of slice regularity to functions of a dual-quaternionic variable [PDF]
, 2021 In this paper, we present the algebraic properties of dual quaternions and define a slice regularity of a dual quaternionic function. Since the product of dual quaternions is non-commutative, slice regularity is derived in two ways.
Ji Eun Kim
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Integral Formulas for a Class of Curvature PDE'S and Application to Isoperimetric Inequalities and to Symmetry Problems [PDF]
, 2007 We prove integral formulas for closed hypersurfaces in C^(n+1); which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then
Martino, Vittorio, Montanari, Annamaria
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Existence and uniqueness of global solutions to fully nonlinear second order elliptic systems [PDF]
, 2016 We consider the problem of existence and uniqueness of strong a.e. solutions u:Rn⟶RNu:Rn⟶RN to the fully nonlinear PDE system F(⋅,D2u)=f, a.e. on Rn,(1) F(⋅,D2u)=f, a.e. on Rn,(1) when f∈L2(Rn)Nf∈L2(Rn)N and F is a Carathéodory map.
A. Buica +33 more
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HYPERHOLOMORPHIC FUNCTIONS WITH VALUES IN A MODIFIED FORM OF QUATERNIONS [PDF]
, 2020 We give the definition of hyperholomorphic pseudocomplex functions, i. e., functions with values in a special form of quaternions, and propose the necessary variables, functions, and Dirac operators to describe the Cauchy integral theorem and the ...
Ji Eun Kim
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Boundedness of the L-index in a direction of entire solutions of second order partial differential equation [PDF]
, 2019 See ...
Bandura, Andriy, Skaskiv, Oleh
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THE CORRESPONDING CAUCHY - RIEMANN SYSTEM FOR DUAL QUATERNION-VALUED FUNCTIONS [PDF]
, 2018 This paper provides differential operators in dual quaternions and represents the regularity of dual quaternionvalued functions using the dual Cauchy - Riemann system in dual quaternions.
Kim J.E.
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