Inequalities between Dirichlet and Neumann eigenvalues of vibrating strings
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-018-0824-9
Abstract: The Dirichlet eigenvalues $${\{\lambda_{n}\}_{n=1}^{\infty}}$${λn}n=1∞ and Neumann eigenvalues $${\{\mu_{n}\}_{n=1}^{\infty}}$${μn}n=1∞ of the string equation $${\varphi'' (x) +\lambda \rho (x) \varphi(x) =0}$$φ′′(x)+λρ(x)φ(x)=0 are considered. It is known that $${ \mu_{n} < \lambda_{n} < \mu_{n+2}}$$μn read more here.
Keywords: lambda; vibrating strings; neumann eigenvalues; eigenvalues vibrating ... See more keywords
Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons
Sign Up to like & getrecommendations! Published in 2018 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2017.12.001
Abstract: Abstract Recently a new transform method, called the Unified Transform or the Fokas method, for solving boundary value problems (BVPs) for linear and integrable nonlinear partial differential equations (PDEs) has received a lot of attention.… read more here.
Keywords: eigenvalues eigenfunctions; computing eigenvalues; laplacian convex; eigenfunctions laplacian ... See more keywords
Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms
Sign Up to like & getrecommendations! Published in 2019 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2019.01.006
Abstract: Abstract In this paper, we study the first eigenvalue of the Dirichlet-to-Neumann operator acting on differential forms of a Riemannian manifold with boundary isometrically immersed in some Euclidean space. We give a lower bound of… read more here.
Keywords: neumann operator; eigenvalue gap; operator acting; dirichlet neumann ... See more keywords
Dirichlet-to-Neumann and elliptic operators on C1+-domains: Poisson and Gaussian bounds
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DOI: 10.1016/j.jde.2019.04.034
Abstract: We prove Poisson upper bounds for the heat kernel of the Dirichlet-to-Neumann operator with variable H{\"o}lder coefficients when the underlying domain is bounded and has a C 1+$\kappa$-boundary for some $\kappa$ > 0. We also… read more here.
Keywords: neumann elliptic; domains poisson; operators domains; poisson gaussian ... See more keywords
L2 estimates for commutators of the Dirichlet-to-Neumann Map associated to elliptic operators with complex-valued bounded measurable coefficients on R+n+1
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125408
Abstract: Abstract In this paper we establish commutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in the upper half-space R + n + 1 : = { ( x , t… read more here.
Keywords: commutators dirichlet; estimates commutators; neumann map; map associated ... See more keywords
Recovering a potential in damped wave equation from Dirichlet-to-Neumann operator
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DOI: 10.1088/1361-6420/abdb41
Abstract: The inverse problem of recovering the potential q(x) in the damped wave equation m(x)utt+μ(x)ut=r(x)uxx+q(x)u , (x, t) ∈ Ω T ≔ (0, ℓ) × (0, T) subject to the boundary conditions u(0, t) = ν(t),… read more here.
Keywords: potential damped; recovering potential; damped wave; equation ... See more keywords
Local Space–Time Dirichlet–Neumann Nonreflecting Boundary Values: Half-Space Spatial Orthogonal Mode Projections
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Antennas and Propagation"
DOI: 10.1109/tap.2018.2862342
Abstract: This paper follows the time-honored analyses to provide a formal bridge connecting the PML and the well-understood (classical) Dirichlet and Neumann boundary value problems. The connection offers many theoretical and practical advantages not immediately obvious… read more here.
Keywords: nonreflecting boundary; dirichlet; space; time ... See more keywords
Application of Dirichlet-to-Neumann Map Boundary Condition for Low-Frequency Electromagnetic Problems
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DOI: 10.1109/tmag.2020.3018482
Abstract: In this article, we present a differential formulation combined with an exact boundary condition based on a Dirichlet-to-Neumann (DtN) operator, and its applications to eddy current problems. A numerical model for the eddy current problem… read more here.
Keywords: boundary condition; application dirichlet; eddy current; neumann map ... See more keywords
Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values
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DOI: 10.1142/s0219530522500026
Abstract: We study the regularity of solutions of the Poisson equation with Dirichlet, Neumann and mixed boundary values in polyhedral cones [Formula: see text] in the specific scale [Formula: see text] of Besov spaces. The regularity… read more here.
Keywords: mixed boundary; equation dirichlet; neumann mixed; dirichlet neumann ... See more keywords
DIRICHLET TO NEUMANN OPERATOR FOR ABELIAN YANG-MILLS GAUGE FIELDS
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Geometric Methods in Modern Physics"
DOI: 10.1142/s0219887817501535
Abstract: We consider the Dirichlet to Neumann operator for abelian YangMills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with… read more here.
Keywords: neumann operator; gauge fields; boundary conditions; operator abelian ... See more keywords
Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations
Sign Up to like & getrecommendations! Published in 2023 at "Mathematics"
DOI: 10.3390/math11092185
Abstract: Dunkl operators are a family of commuting differential–difference operators associated with a finite reflection group. These operators play a key role in the area of harmonic analysis and theory of spherical functions. We study the… read more here.
Keywords: problems dunkl; neumann boundary; dunkl polyharmonic; dirichlet neumann ... See more keywords