Zobrazeno 1 - 10
of 169
pro vyhledávání: '"Lamberti, PIER DOMENICO"'
We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide Hadamard-ty
Externí odkaz:
http://arxiv.org/abs/2410.19960
We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn inequality doesn't hold.
Comment: references added; 9 pages, 2 figu
Comment: references added; 9 pages, 2 figu
Externí odkaz:
http://arxiv.org/abs/2409.07206
Autor:
Lamberti, Pier Domenico, Moroz, Vitaly
We study sub and supersolutions for the $p$-Laplace type elliptic equation of the form $$-\Delta_p u-V|u|^{p-2}u=0\quad\text{in $\Omega$},$$ where $\Omega$ is a radially symmetric domain in ${\mathbb{R}}^N$ and $V(x)\ge 0$ is a continuous potential s
Externí odkaz:
http://arxiv.org/abs/2405.16705
We consider Campanato spaces with exponents $\lambda , p$ on domains of class $C^{0,\gamma}$ in the N-dimensional Euclidean space endowed with a natural anisotropic metric depending on $\gamma$. We discuss several results including the appropriate Ca
Externí odkaz:
http://arxiv.org/abs/2302.11990
After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning natural St
Externí odkaz:
http://arxiv.org/abs/2206.00505
We prove spectral stability results for the $curl curl$ operator subject to electric boundary conditions on a cavity upon boundary perturbations. The cavities are assumed to be sufficiently smooth but we impose weak restrictions on the strength of th
Externí odkaz:
http://arxiv.org/abs/2201.12924
This paper investigates the stability properties of the spectrum of the classical Steklov problem under domain perturbation. We find conditions which guarantee the spectral stability and we show their optimality. We emphasize the fact that our spectr
Externí odkaz:
http://arxiv.org/abs/2103.04991
Publikováno v:
Calc. Var. (2019) 58:33
We study the spectral stability of two fourth order Steklov problems upon domain perturbation. One of the two problems is the classical DBS - Dirichlet Biharmonic Steklov - problem, the other one is a variant. Under a comparatively weak condition on
Externí odkaz:
http://arxiv.org/abs/2103.04202
We consider the spectral problem for the Grushin Laplacian subject to homogeneous Dirichlet boundary conditions on a bounded open subset of $\mathbb{R}^N$. We prove that the symmetric functions of the eigenvalues depend real analytically upon domain
Externí odkaz:
http://arxiv.org/abs/2009.03130
We discuss a Steklov-type problem for Maxwell's equations which is related to an interior Calder\'{o}n operator and an appropriate Dirichlet-to-Neumann type map. The corresponding Neumann-to-Dirichlet map turns out to be compact and this provides a F
Externí odkaz:
http://arxiv.org/abs/2007.10765