On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori
, 2015 In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tori. We present two results.
Léna, Corentin
core
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
Spectra of graph neighborhoods and scattering
, 2007 Let $(G_\epsilon)_{\epsilon>0}$ be a family of '$\epsilon$-thin' Riemannian manifolds modeled on a finite metric graph $G$, for example, the $\epsilon$-neighborhood of an embedding of $G$ in some Euclidean space with straight edges.
Grieser, Daniel
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Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold [PDF]
, 2007 For any bounded regular domain $\Omega$ of a real analytic Riemannian manifold $M$, we denote by $\lambda_{k}(\Omega)$ the $k$-th eigenvalue of the Dirichlet Laplacian of $\Omega$.
Ilias, Saïd, Soufi, Ahmad El
core +3 more sources
Positive Eigenfunctions of a Schrödinger Operator [PDF]
, 2017 The paper considers the eigenvalue problem -Δu-αu+λg(x)u=0 withu∈H1(RN),u≠0 where ∞, λ ∈ and g(x)≡0 on Ω¯, g(x) ∈ (0,1] onRN \ Ω¯ and lim|x|→+∞g(x)=1 for some bounded open set Ω∈RN. Given α>0, does there exist a value of λ>0 for which the problem has
Stuart, C. A., Zhou, Huan-Song
core
The Perturbed Maxwell Operator as Pseudodifferential Operator
, 2013 As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in d = 3 can be seen as a pseudodifferential operator. This necessitates a better understanding of the periodic Maxwell operator M_0.
De Nittis, Giuseppe, Lein, Max
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New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation. [PDF]
Springerplus, 2014 Roshid HO +4 more
europepmc +1 more source
Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method. [PDF]
Springerplus, 2014 Roshid HO +3 more
europepmc +1 more source
Exact traveling wave solutions for system of nonlinear evolution equations. [PDF]
Springerplus, 2016 Khan K, Akbar MA, Arnous AH.
europepmc +1 more source
Spectral analysis of a Stokes-type operator arising from flow around a rotating body
, 2011 R. Farwig, Š. Nečasová, J. Neustupa
semanticscholar +1 more source