共查询到20条相似文献,搜索用时 15 毫秒
1.
Alberto Damiano 《Advances in Applied Clifford Algebras》2007,17(3):343-355
This paper is a short report on the generalization of some results of our previous paper [12] to the case of spin j/2 Dirac operators in real dimension three for arbitrary odd integer j. We use an explicit formula for the local expression of such operators to study their algebraic properties, construct the
compatibility conditions of the overdetermined system associated to the operator in several spatial variables, and we prove
that its associated algebraic complex, dual do the BGG sequence coming from representation theory, has substantially the same
pattern as the Cauchy-Fueter complex.
The author is a member of the Eduard Čech Center and his research is supported by the relative grants. 相似文献
2.
Peter Franek 《Advances in Applied Clifford Algebras》2007,17(3):469-480
In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model G/P of a Cartan geometry. The first operator in this sequence is locally the Dirac operator in 2 Clifford variables, D = (D
1, D
2), where D
i
= ∑
j
e
j
. ∂
ij
. It follows from the construction that this operator is invariant with respect to the action of the group G. There are 2 other G-invariant differential operators following it so that the sequence of operators is exact. We compute the local expression
of these operators and show that it coincides with the operators described in [2, 5, 6] by the tools of Clifford analysis.
However, it follows from our approach that the operators are invariant.
The work presented here was supported by the grants GAUK 447/2004 and GA ČR 201/05/H005. 相似文献
3.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
4.
5.
A new Cauchy-type formula for hypermonogenic functions is derived. Hypermonogenic functions, introduced in [6], are a generalization
of holomorphic functions to several dimensions. The power function xm is hypermonogenic.
This paper is dedicated to the memory of our friend and colleague Jarolim Bureš 相似文献
6.
The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are
not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on .
Received: October, 2007. Accepted: February, 2008. 相似文献
7.
We study the existence of solutions of control problems relative to a nonlinear elliptic system with Dirichlet boundary conditions.
In this problem, the control variables are the coefficients of the equations and the open set where they are posed. It is
known that this class of problems has no solution in general, but using homogenization results about elliptic systems we show
the existence of solutions when the controls are searched in a bigger set. These results are related to the selection of optimal
materials and shapes. 相似文献
8.
Alessandro Perotti 《Advances in Applied Clifford Algebras》2009,19(2):441-451
We study Fueter-biregular functions of one quaternionic variable. We consider left-regular functions in the kernel of the
Cauchy–Riemann operator
. A quaternionic function is biregular if on Ω, f is invertible and . Every continuous map p from Ω to the sphere of unit imaginary quaternions induces an almost complex structure Jp on the tangent bundle of . Let be the space of (pseudo)holomorphic maps from (Ω, Jp) to (), where Lp is the almost complex structure defined by left multiplication by p. Every element of is regular, but there exist regular functions that are not holomorphic for any p. The space of biregular functions contains the invertible elements of the spaces . By means of a criterion, based on the energy-minimizing property of holomorphic maps, that characterizes holomorphic functions
among regular functions, we show that every biregular function belongs to some space .
Received: October, 2007. Accepted: February, 2008. 相似文献
9.
Massimo Grossi 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):227-241
Let Ω be a smooth bounded domain of
with N ≥ 5. In this paper we prove, for ɛ > 0 small, the nondegeneracy of the solution of the problem
under a nondegeneracy condition on the critical points of the Robin function. Our proof uses different techniques with respect
to other known papers on this topic. 相似文献
10.
Ricardo Abreu Blaya Juan Bory Reyes Tania Moreno García 《Complex Analysis and Operator Theory》2007,1(3):301-305
In the present paper we provide some conditions of a geometrical character for continuous extendibility of the Clifford–Cauchy
transform to the boundary of a domain in the Euclidean space of higher dimensions if its density satisfies a H?lder condition.
The criterion obtained in this work is an extension to a very general class of domains of a result, which has already become
classical, obtained by Viorel Iftimie, who proved in 1965, for the case of a domain with compact Liapunov boundary, that the
Clifford–Cauchy transform has H?lder–continuous limit values for any H?lder–continuous density.
Received: August 15, 2006. Accepted: November 2, 2006. 相似文献
11.
In this paper we give a generalization of the classical Borel–Carathéodory theorem in complex analysis to higher dimensions
in the framework of Quaternionic Analysis.
Submitted: November 14, 2007., Revised: February 25, 2008. 相似文献
12.
Giovanna Cerami 《Milan Journal of Mathematics》2006,74(1):47-77
In this paper the results of some investigations concerning nonlinear elliptic problems in unbounded domains are summarized
and the main difficulties and ideas related to these researches are described.
The model problem
where
, N ≥ 3, is an unbounded smooth domain, a(x) is a smooth real function defined on Ω, such that
, is considered and existence and multiplicity results are given under various assumptions on Ω.
Work supported by national research project “Metodi variazionali e topologici nello studio di fenomeni non lineari".
Lecture held in the Seminario Matematico e Fisico on February 28, 2005
Received: June 2006 相似文献
13.
Victor Palamodov 《Advances in Applied Clifford Algebras》2009,19(2):417-425
The paper addresses the Levi problem for a system of n Fueter equations in a domain in quaternionic space . This problem relates to various conditions of convexity and pseudoconvexity of the boundary of the domain.
Received: October, 2007, Accepted: February, 2008. 相似文献
14.
In this paper, we study a system of elliptic equations by applying the Limit Index Theory. Under some assumptions on nonlinear
part, we can obtain the existence of multiple solutions for the equations.
The research is supported by NNSF of China (10471024) and Fujian Provincial Natural Science Foundation of China (A0410015). 相似文献
15.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(2):145-152
Starting with an integral representation for the class of continuously differentiable solutions
of the system
where
is the complex Clifford algebra constructed over
are some suitable Clifford vectors and
their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae.
Some consequences of this result are also derived. 相似文献
16.
We discuss explicit boundary value problems for solutions of the Fueter equation in which are normally solvable. The results extend to nonlinear first order elliptic systems.
Received: October, 2007, Accepted: February, 2008. 相似文献
17.
We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann
transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space.
Received: May 11, 2007. Revised: May 20, 2008. Accepted: May 23, 2008. 相似文献
18.
N. M. Ivochkina 《Journal of Fixed Point Theory and Applications》2008,4(1):47-56
We adapt to degenerate m-Hessian evolution equations the notion of m-approximate solutions introduced by N. Trudinger for m-Hessian elliptic equations, and we present close to necessary and sufficient conditions guaranteeing the existence and uniqueness
of such solutions for the first initial boundary value problem.
Dedicated to Professor Felix Browder 相似文献
19.
Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W
r
+ W
r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w
r
+ w
r+2 satisfies in Ω the system d
*
w
r
= 0, dw
r
+ d
*
w
r+2 = 0; dw
r+2 = 0.
Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure
theorem is proved for the solutions of the Moisil-Théodoresco system.
相似文献
20.
Thomas Schmidt 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):109-129
We consider multi-dimensional variational integrals
where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial -regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring’s lemma, and establishes partial regularity with the optimal H?lder exponent
α in a single step.
相似文献