On the numerical solutions of convection-diffusion equations
On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
On the Principal Eigenvalue of a Second Order Linear Elliptic Problem with an Indefinite Weight Function.
On the Rate of Convergence of the Preconditioned Conjugate Gradient Method.
On the regularity of elliptic differential equations using symmetry techniques and suitable discrete spaces.
On the regularity of solutions to a nonvariational elliptic equation
On the Relation between the S-matrix and the Spectrum of the Interior Laplacian
The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.
On the relationship between difference and projection-difference methods
On the Relative Completeness of the Generalized Eigenvectors of Elliptic Eigenvalue Problems with Indefinite Weight Functions.
On the Riemann-Hilbert problem in the domain with a nonsmooth boundary.
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering.
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators.
On the solution of some non-local problems
This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these...
On the solution of the Dirichlet problem for an elliptic equation degenerating on the boundary.
On the solvability of degenerated quasilinear elliptic problems.
On the super-approximation property of Galerkin's method with finite elements.
On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices.
On traces of solutions of a semilinear partial differential equation of elliptic type
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.