The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The laplacian and the discrete laplacian
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.
The limiting equation for Neumann Laplacians on shrinking domains.
The method of fictitious right-hand sides
The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices...
The Method of Lines for Poisson's Equation with Nonlinear or Free Boundary Conditions.
The mixed problem for the Laplace equation on the rectangle
The N-Dimensional Cauchy-Riemann equations.
The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves.
The Neumann problem for the Laplace equation on general domains
The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on . If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on a necessary and sufficient condition for the solvability...
The Numerical Solution Of Elliptic Partial Differential Equations By The Method Of Lines.
The Ordering of Tridiagonal Matrices in the Cyclic Reduction Method for Poisson's Equation.
The point on the simple Molodensky’s problem
Il problema di Molodensky, in approssimazione sferica è detto «semplice» perchè può essere trasformato da problema di derivata obliqua a problema di Dirichlet per l’operatore di Laplace. Tale problema è accuratamente analizzato in questa Nota, con particolare riguardo alla generalizzazione delle condizioni di regolarità soddisfatte dal contorno , sufficienti a garantire l’esistenza di una soluzione fisicamente accettabile.
The point source function of the mixed difference problem in the half-plane
The Poisson equation in homogeneous Sobolev spaces.
The regularity of weak and very weak solutions of the Poisson equation on polygonal domains with mixed boundary conditions (part I)
We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.
The regularity of weak and very weak solutions of the Poisson equation on polygonal domains with mixed boundary conditions (part II)
We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.
The Sinc Method in Multiple Space Dimensions: Model Probelms.
The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks.
The Stefan problem with kinetic condition at the free boundary