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The convergence of the finite element solution for the second order elliptic problem in the $n$ -dimensional bounded domain $(n \geq 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^{1}$ and $L_{2}$ norms are obtained.

The first boundary problem for a degenerate elliptic system.

Devdariani, G. (2001)

Bulletin of TICMI

The first eigenvalue for the $p$ -Laplacian operator.

Ly, Idrissa (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

The first eigenvalue of $p$ -Laplacian systems with nonlinear boundary conditions.

Kandilakis, D.A., Magiropoulos, M., Zographopoulos, N.B. (2005)

Boundary Value Problems [electronic only]

The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya, Igor Verbitsky (2004)

Annales de l’institut Fourier

We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on $ℝ^{n}$ for the relativistic Schrödinger operator $\sqrt{- Δ} + Q$ to be bounded as an operator from the Sobolev space $W_{2}^{1 / 2} (ℝ^{n})$ to its dual $W_{2}^{- 1 / 2} (ℝ^{n})$ .

The free laplacian with attractive boundary conditions

H. Englisch, M. Schröder, P. Šeba (1987)

Annales de l'I.H.P. Physique théorique

The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method.

Wolfgang Hackbusch (1992)

Numerische Mathematik

The Frequency Decomposition Multi-Grid Method. Part I: Application to Anisotropic Equations.

Wolfgang Hackbusch (1989/1990)

Numerische Mathematik

The functional calculus for the laplacian on Lipschitz domains

David Jerison, Carlos E. Kenig (1989)

Journées équations aux dérivées partielles

The $(G^{'} / G)$ -expansion method for solving the combined and the double combined sinh-cosh-Gordon equations.

Kheiri, H., Jabbari, A. (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

The G method for heterogeneous anisotropic diffusion on general meshes

Léo Agélas, Daniele A. Di Pietro, Jérôme Droniou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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

Haizhong Li, Linlin Su (2005)

Banach Center Publications

We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in $R^{N}$ 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.

Joel L. Weiner (1984)

Mathematische Annalen

The general form of local bilinear functions

Milan Práger (1993)

Applications of Mathematics

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 $L_{2} (a, b)$ and $H^{1} (a, b)$ is given.

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