Angelica Malaspina

ON AN INTEGRAL EQUATION OF THE FIRST KIND ARISING IN THE THEORY OF COSSERAT

In this paper we study an integral equation of the first kind concerning an indirect boundary integral method for the Dirichlet problem in the theory of Cosserat continuum. Our method hinges on the theory of reducible operators and on the theory of differential forms.

On the Dirichlet and the Neumann problems for Laplace equation in multiply connected domains

In the classical indirect methods, the Dirichlet and the Neumann problems for Laplace equation are solved by means of a double and a simple layer potential, respectively. In this article we propose a method for obtaining the solutions of these problems in a multiply connected bounded domain of ℝ n (n ≥ 2) using different integral representations. Namely, we solve the Dirichlet problem by means of a simple layer potential and the Neumann problem through a double layer potential. An application in the theory of conjugate differential forms is also presented.

On the Dirichlet Problem for the Stokes System in Multiply Connected Domains

The Dirichlet problem for the Stokes system in a multiply connected domain of is considered in the present paper. We give the necessary and sufficient conditions for the representability of the solution by means of a simple layer hydrodynamic potential, instead of the classical double layer hydrodynamic potential.

Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains

The present paper is concerned with an indirect method to solve the Dirichlet and the traction problems for Lamé system in a multiply connected bounded domain of ℝn, n ≥ 2. It hinges on the theory of reducible operators and on the theory of differential forms. Differently from the more usual approach, the solutions are sought in the form of a simple layer potential for the Dirichlet problem and a double layer potential for the traction problem.2000 Mathematics Subject Classification. 74B05; 35C15; 31A10; 31B10; 35J57.

The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz

We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains of () with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.

Integral Representation for the Solution of Dirichlet Problem for the Stokes System

The present paper is concerned with an indirect method to solve the Dirichlet boundary value problem for the Stokes system in a multiply connected bounded domain Ω of Rn, n≥2, with the datum in [W1,p(∂Ω)]n. The solution is sought in the form of a simple layer hydrodynamic potential. The method hinges on the theory of reducible operators and on the theory of differential forms. It does not require the use of pseudo‐differential operators.

Regularization of Some Integral Equations of the First Kind

Results concerning the regularization of some integral equations of the first kind involved in the study of BVPs for different PDEs in simply connected domains and in multiply connected domains are presented.

An Indirect Boundary Integral Equation Method for Boundary Value Problems in Elastostatics

In this paper we describe an indirect boundary integral equations method to solve the Dirichlet problem for Lame system in a multiply connected domain of \(\mathbb{R}^{n}\), n ≥ 2. In particular we show how to represent the solution in terms of a single-layer potential, instead of the classical double-layer potential. By using the theory of reducible operators and the theory of differential forms we treat also the double-layer potential ansatz for the traction problem.