Results 41 to 50 of about 358 (72)
On Courant's nodal domain property for linear combinations of eigenfunctions, Part I [PDF]
, 2018 According to Courant's theorem, an eigenfunction as\-sociated with the $n$-th eigenvalue $\lambda\_n$ has at most $n$ nodal domains. A footnote in the book of Courant and Hilbert, states that the same assertion is true for any linear combination of ...
Bérard, Pierre, Helffer, Bernard
core +3 more sources
Uniqueness and stability results for an inverse spectral problem in a periodic waveguide
, 2015 Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$.
Kavian, Otared +2 more
core +3 more sources
Sharp boundary estimates for elliptic operators [PDF]
arXiv, 1998 We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on the change of the eigenvalues when the region is reduced slightly in size, subject to DBCs.
arxiv
Pseudospectra of semi-classical (pseudo)differential operators [PDF]
Comm. Pure and Appl. Math. 57 (2004), no. 3, 384-415., 2003 The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.
arxiv
Boundedness of maximal functions on non-doubling manifolds with ends
, 2013 Let $M$ be a manifold with ends constructed in \cite{GS} and $\Delta$ be the Laplace-Beltrami operator on $M$. In this note, we show the weak type $(1,1)$ and $L^p$ boundedness of the Hardy-Littlewood maximal function and of the maximal function ...
Duong, Xuan Thinh, Li, Ji, Sikora, Adam
core
Refined geometric L^p Hardy inequalities [PDF]
arXiv, 2003 For a bounded convex domain \Omega in R^N we prove refined Hardy inequalities that involve the Hardy potential corresponding to the distance to the boundary of \Omega, the volume of $\Omega$, as well as a finite number of sharp logarithmic corrections. We also discuss the best constant of these inequalities.
arxiv
Partial Differential Equations in Applied MathematicsThe Bogoyavlenskii and the simplified modified Camassa-Holm (SMCH) models are studied through the recent technique namely auxiliary equation method in this paper.
M. Ashikur Rahman +6 more
doaj
Billiards and boundary traces of eigenfunctions [PDF]
arXiv, 2003 This is a report for the 2003 Forges Les Eaux PDE conference on recent results with A. Hassell on quantum ergodicity of boundary traces of eigenfunctions on domains with ergodic billiards, and of work in progress with Hassell and Sogge on norms of boundary traces. Related work by Burq, Grieser and Smith-Sogge is also discussed.
arxiv
Partial Differential Equations in Applied MathematicsThis study investigate the widely used nonlinear fractional Kairat-II (K-II) model, which is used to explain the differential geometry of curves and equivalence aspects.
M. Al-Amin, M. Nurul Islam, M. Ali Akbar
doaj
Generic spectral simplicity of polygons [PDF]
arXiv, 2007 We study the Laplace operator with Dirichlet or Neumann boundary condition on polygons in the Euclidean plane. We prove that almost every simply connected polygon with at least four vertices has simple spectrum. We also address the more general case of geodesic polygons in a constant curvature space form.
arxiv