The index of isolated critical points and solutions of elliptic equations in the plane
The inverse problem for elliptic equations from Dirichlet to Neumann map in multiply connected domains.
The -Helmholtz projection in finite cylinders
In this article we prove for the existence of the -Helmholtz projection in finite cylinders . More precisely, is considered to be given as the Cartesian product of a cube and a bounded domain having -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in is solved, which implies existence and a representation of the -Helmholtz projection as...
The Lane-Emden Function and Nonlinear Eigenvalues Problems
We consider a semilinear elliptic eigenvalues problem on a ball of and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.
The L.P.D.E.M., a mixed finite difference method for elliptic problems.
The maximum principle for equations with composite coefficients.
The mortar element method for three dimensional finite elements
The Mortar method in the wavelet context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
The Mortar Method in the Wavelet Context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
The Neumann problem for elliptic equations with non-smooth coefficients.
The Neumann problem for some degenerate elliptic equations
In the paper we study the equation , where is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set . We prove existence and uniqueness of solutions in the space for the Neumann problem.
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 Neumann-Dirichlet Domain Decomposition Method with Inexact Solvers on the Subdomains.
The nonexistence of a weak solution of Dirichlet's problem for the functional of minimal surface on nonconvex domains
The nonlinear Neumann problem and sharp weighted Sobolev inequalities
We prove sharp inequalities in weighted Sobolev spaces. Our approach is based on the blow-up technique applied to some nonlinear Neumann problems.
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures
We investigate the effect of admitting signed measures as a datum at the scalar Chern-Simons equation with the Dirichlet boundary condition. Approximating by a sequence of functions or finite signed measures such that this equation has a solution for each , we are interested in establishing the convergence of the sequence to a function and describing the form of the measure which appears on the right-hand side of the scalar Chern-Simons equation solved by .
The numerical solution of large finite element systems by explicit preconditioning semi-direct methods
The Oblique Derivative Problem. I.
The optimization of the stationary heat equation with a variable right-hand side
Solving the stationary heat equation we optimize the temperature on part of the boundary of the domain under investigation. First the Poisson equation is solved; both the Neumann condition on part of the boundary and the Newton condition on the rest are prescribed, the distribution of the heat sources being variable. In the second case, the heat equation also contains a convective term, the distribution of heat sources is specified and the Neumann condition is variable on part of the boundary.