The Absolute Continuity of Elliptic Measure Revisited.
The analysis of intergrid transfer operators and multigrid methods for nonconforming finite elements.
The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form
2000 Mathematics Subject Classification: 35J70, 35P15.The asymptotic of the first eigenvalue for linear second order elliptic equations in divergence form with large drift is studied. A necessary and a sufficient condition for the maximum possible rate of the first eigenvalue is proved.
The block-grid method for solving Laplace's equation on polygons with nonanalytic boundary conditions.
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
The Calderón problem with partial data
We describe a joint work with C.E. Kenig and G. Uhlmann [9] where we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension , the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem.
The Calderón Projector for an Elliptic Operator in Divergence Form.
The change in electric potential due to lightning
The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the...
The classical and the modified Neumann problems for the inhomogeneous pluriholomorphic system in polydiscs.
The Convergence of Spline Collocation for Strongly Elliptic Equations on Curves.
The Convergence rate and Complexity of Precondotioned Iterative methods based on Approximate finite Element matrix Factorization
The current situation in the linear problem of Molodenskii.
Si studiano le condizioni per 1’esistenza, l’unicità e la stabilità della soluzione debole del problema lineare di Molodenskii in approssimazione quasi-sferica, generalizzando una tecnica perturbativa usata in precedenza per la soluzione di tipo classico. La procedura seguita richiede delle condizioni di maggior regolarità per il contorno, di quelle usate nell’analisi del problema «semplice». Il risultato ottenuto è l'esistenza e unicità di una soluzione con derivate seconde a quadrato integrabile,...
The density of solenoidal functions and the convergence of a dual finite element method
A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.
The Dirchlet Problem for a Complex Monge-Ampère Equation.
The Dirichlet boundary value problem for certain Schrödinger equations with magnetic vector potentials
The probabilistic approach to the Dirichlet boundary value problem for certain Schrödinger equations with magnetic vector potentials is examined
The Dirichlet problem for a singular elliptic equation
We study the solvability of the Dirichlet problem for a linear elliptic operator of the second order in which the coefficients of the first order derivatives become infinite on a portion of the boundary. The study makes use of Schauder’s estimates and suitably constructed barriers.
The Dirichlet problem for elliptic equations in the plane
In this paper an existence and uniqueness theorem for the Dirichlet problem in for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class VMO.
The Dirichlet problem in half-space for elliptic equations with unbounded coefficients
The Dirichlet problem in the dispersion of gas exhalations over a wet hilly surface
The Dirichlet problem in weighted spaces on a dihedral domain
We examine the Dirichlet problem for the Poisson equation and the heat equation in weighted spaces of Kondrat'ev's type on a dihedral domain. The weight is a power of the distance from a distinguished axis and it depends on the order of the derivative. We also prove a priori estimates.