11 citations · 30 across the 15 of their papers we have counts for
16 papers
The Dirichlet problem for a non-commutative elliptic operator in the ball
A. Moreno García, D. Alfonso Santiesteban, R. Abreu Blaya
In this paper we establish a necessary and sufficient condition for the solvability of the Dirichlet problem in the unit ball for the second order system $\partial_{\u…
Revisiting Fischer decompositions by inframonogenic functions
Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Juan Bory Reyes +1
We explore Fischer decompositions from the perspective of inframonogenic functions in Clifford analysis, a non-commutative version of harmonic functions in Euclidean spaces. We stu…
Magnetic Dirichlet Laplacian on a perturbed twisted tube
Diana Barseghyan, Ricardo Abreu Blaya, Juan Bory-Reyes +1
It is well known that the spectrum of the Dirichlet Laplacian for a compact perturbation of a three-dimensional, periodically twisted tube is unstable with respect to domain deform…
Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions
Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Daniel Alpay
The Clifford algebra language allows us to rewrite the Lamé-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is w…
Constructing steering-type solutions for higher order Cauchy-Riemann equations in
Daniel Alfonso Santiesteban, Dixan Peña Peña, Ricardo Abreu Blaya
The multidimensional Cauchy-Riemann operator provides a framework for studying higher order partial differential equations in , whose solutions include polymonoge…
Jump problem for generalized Lamé-Navier systems in
Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Daniel Alpay
This paper is devoted to study a fundamental system of equations in Linear Elasticity Theory: the famous Lamé-Navier system. The Clifford algebra language allows us to rewrite this…
Hardy decomposition of higher order Lipschitz classes by polymonogenic functions
Lianet De la Cruz Toranzo, Ricardo Abreu Blaya, Swanhild Bernstein
In this paper we find a decomposition of higher order Lipschitz functions into the traces of a polymonogenic function and solve a related Riemann-Hilbert problem. Our approach lies…
Decomposition of first order Lipschitz functions by Clifford algebra-valued harmonic functions
Lianet De la Cruz Toranzo, Ricardo Abreu Blaya, Swanhild Bernstein
In this paper we solve the problem on finding a sectionally Clifford algebra-valued harmonic function, zero at infinity and satisfying certain boundary value condition related to h…
Stolarsky-Puebla index
J. A. Mendez-Bermudez, R. Aguilar-Sanchez, Ricardo Abreu Blaya +1
We introduce a degree-based variable topological index inspired on the Stolarsky mean (known as the generalization of the logarithmic mean). We name this new index as the Stolarsky…
Generalizations of harmonic functions in
Daniel Alfonso Santiesteban, Yudier Peña Pérez, Ricardo Abreu Blaya
In recent works, arbitrary structural sets in the non-commutative Clifford analysis context have been used to introduce non-trivial generalizations of harmonic Clifford algebra val…
On a Generalized Lamé-Navier system in
Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Martín Patricio Árciga Alejandre
This paper is devoted to a fundamental system of equations in Linear Elasticity Theory: the famous Lamé-Navier system. The Clifford algebra language allows us to rewrite this syste…
On a Riemann-Hilbert boundary value problem for -harmonic functions in
José Luis Serrano Ricardo, Ricardo Abreu Blaya, Juan Bory Reyes +1
The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for -harmonic functions, which are linked with the use of two orthogonal basis of the…
On the plane Lamé-Navier system in fractal domains
Diego Esteban Gutierrez Valencia, Ricardo Abreu Blaya, Martín Patricio Árciga Alejandre +1
This paper is devoted to study a fundamental system of equations in plane Linear Elasticity Theory, the two-dimensional Lamé-Navier system. We rewrite them in a compressed form in…
Polyanalytic Hardy decomposition of higher order Lipschitz functions
Ricardo Abreu Blaya, Lianet De la Cruz Toranzo
This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve into a sum of two polyanalytic functions in each open domain…
On Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras
Carlos Daniel Tamayo Castro, Ricardo Abreu Blaya, Juan Bory Reyes
In this paper, we mainly consider the Riemann boundary value problems for lower dimensional non-commutative Clifford algebras valued monogenic functions. The solutions are given in…
Biquaternionic Reformulation of a Fractional Monochromatic Maxwell System
Yudier Peña Pérez, Ricardo Abreu Blaya, Martín Patricio Árciga Alejandre +1
In this work we propose a biquaternionic reformulation of a fractional monochromatic Maxwell system. Additionally, some examples are given to illustrate how the quaternionic fracti…