A remark on the solvability of the Dirichlet problem in Sobolev spaces with power-type weights
A remark on two dimensional periodic potentials.
A remark on uniqueness for quasilinear elliptic equations
A Remark to a Paper of Kato and Ikebe.
A representation formula for radially weighted biharmonic functions in the unit disc.
A result on the bifurcation from the principal eigenvalue of the -Laplacian.
A Right-Inverse for the Divergence Operator in Spaces of Piecewise Polynomials. Application to the p-Version of the Finite Element Method
A robust and parallel multigrid method for convection diffusion equations.
A saddle point theorem for non-smooth functionals and problems at resonance.
A second eigenvalue bound for the Dirichlet-Schrödinger equation with a radially symmetric potential.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H1-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A semilinear control problem involving homogenization.
A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model.
A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential.
A semi-linear problem for the Heisenberg laplacian
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A shape optimization approach for a class of free boundary problems of Bernoulli type
We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.
A sharp result on the poles localization for a Gevrey convex body
In this talk we extend to Gevrey-s obstacles with a result on the poles free zone due to J. Sjöstrand [8] for the analytic case.