On the location of spectral edges in $\mathbb{Z}$-periodic media
, 2010 Periodic $2$nd order ordinary differential operators on $\R$ are known to have the edges of their spectra to occur only at the spectra of periodic and antiperiodic boundary value problems.
Exner, Pavel +2 more
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Reaction-diffusion problems on time-dependent Riemannian manifolds: stability of periodic solutions
, 2017 We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time.
Bandle, Catherine +2 more
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Isoperimetric inequalities for some integral operators arising in potential theory [PDF]
, 2017 In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a ...
EM Harrell +21 more
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On the torsion function with Robin or Dirichlet boundary conditions
, 2013 For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2} \frac{\partial u}{
Berg, M. van den, Bucur, D.
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, 2006 Estimates are obtained for the expected volume of intersection of independent Wiener sausages in Euclidean space in the small time limit. The asymptotic behaviour of the weighted diagonal heat kernel norm on compact Riemannian manifolds with smooth ...
Berg, M. van den, Gilkey, P.
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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
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On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern -- [PDF]
, 2014 In the case of the sphere and the square, Antonie Stern (1925) claimed in her PhD thesis the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with two nodal domains. These two statements were given
Bérard, Pierre, Helffer, Bernard
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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
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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
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Heat trace asymptotics with singular weight functions II
, 2010 We study the weighted heat trace asymptotics of an operator of Laplace type with mixed boundary conditions where the weight function exhibits radial blowup.
Berg, Michiel van den +2 more
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