A method of BAZLEY-FOX type for the eingenvalues of the LAPLACE operator
A method of symmetrization ; Applications to heat and spectral estimates
A minimax formula for the principal eigenvalues of Dirichlet problems and its applications.
A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
A minorization of the first positive eigenvalue of the scalar laplacian on a compact Riemannian manifold [Book]
A Multiscale Enrichment Procedure for Nonlinear Monotone Operators
In this paper, multiscale finite element methods (MsFEMs) and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. In the process, existing work on linear problems [Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Submitted.; Y. Efendiev, J. Galvis and X. Wu, J. Comput. Phys. 230 (2011) 937–955; J. Galvis and...
A non elliptic spectral problem related to the analysis of superconducting micro-strip lines
This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that is unbounded from below and that it has a sequence of negative eigenvalues tending to . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...
A non elliptic spectral problem related to the analysis of superconducting micro-strip lines
This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some...
A nonlinear adaptative multiresolution method in finite differences with incremental unknowns
A nonlinear boundary problem involving the -bi-Laplacian operator.
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
In this paper we study the Sobolev trace embedding W1,p(Ω) → LpV (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λk / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the...
A nonlinear operator in potential theory
A note on Hayman's theorem on the bass note of a drum.
A note on quasilinear elliptic eigenvalue problems.
A note on resonant frequencies for a system of elastic wave equations.
A note on the effect of numerical quadrature in finite element eigenvalue approximation.
A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp.
A one dimensional Hammerstein problem.
A proof of monotony of the Temple quotients in eigenvalue problems
If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue , the sequences of the so-called Schwarz quatients (which are upper bounds for ) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper “Die Monotonie der Templeschen Quotienten” (ZAMM, in print). In the present...
A rapid convergence method for a singular perturbation problem