The exterior Dirichlet problem for quasi linear elliptic equations with small boundary data.
The Feynman path integral as an improper integral over the Sobolev space
The finite element method for nonlinear elliptic equations with discontinuous coefficients.
The Finite Element Method with Lagrangian Multipliers.
The Finite Element Method with Non-Uniform Mesh Sizes Applied to the Exterior Helmholtz Problem.
The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
The finite element solution of second order elliptic problems with the Newton boundary condition
The convergence of the finite element solution for the second order elliptic problem in the -dimensional bounded domain with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the and norms are obtained.
The first boundary problem for a degenerate elliptic system.
The first eigenvalue for the -Laplacian operator.
The first eigenvalue of -Laplacian systems with nonlinear boundary conditions.
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The free laplacian with attractive boundary conditions
The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method.
The Frequency Decomposition Multi-Grid Method. Part I: Application to Anisotropic Equations.
The functional calculus for the laplacian on Lipschitz domains
The -expansion method for solving the combined and the double combined sinh-cosh-Gordon equations.
The G method for heterogeneous anisotropic diffusion on general meshes
In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity,...
The gaps in the spectrum of the Schrödinger operator
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
The Gauss Map for Surfaces in 4-Space.
The general form of local bilinear functions
The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces and is given.