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Letters in Mathematical Physics, ISSN 0377-9017, 8/2018, Volume 108, Issue 8, pp. 1837 - 1849
A system composed of an ideal gas of N fermions interacting with an impurity particle in two space dimensions is considered. The interaction between impurity... 
Geometry | Energy estimates | 35P15 | Theoretical, Mathematical and Computational Physics | Complex Systems | Point interactions | Group Theory and Generalizations | 81V70 | Ultracold Fermi gas | Fermi polaron | Physics | PARTICLE | PHYSICS, MATHEMATICAL | Analysis | Force and energy
Journal Article
Proceedings of the London Mathematical Society, ISSN 1460-244X, 2019, Volume 119, Issue 3, pp. 654 - 680
We consider a variational problem associated with the minimal speed of pulsating traveling waves of the equation ut=uxx+b(x)(1−u)u, x∈R,t>0, where the... 
35C07 (secondary) | 35P15 (primary) | 49R05 | 92D40 | MATHEMATICS | FRAGMENTED ENVIRONMENT MODEL | DIFFUSION
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2016, Volume 366, Issue 3, pp. 1035 - 1066
Let $$\varphi : M^m \rightarrow N^n$$ φ : M m → N n be a minimal, proper immersion in an ambient space suitably close to a space form $$\mathbb {N}^n_k$$ N k n... 
Mathematics, general | Mathematics | 58C21 | 35P15 | 58J50 | NONNEGATIVE RICCI CURVATURE | LAPLACIAN | MATHEMATICS | FINITENESS | REGULARITY | HYPERSURFACES | GAP THEOREMS | EUCLIDEAN-SPACE | HYPERBOLIC SPACE | COMPLETE RIEMANNIAN MANIFOLD | SURFACES | Mathematics - Differential Geometry
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 7, pp. 1233 - 1275
We show that families of coverings of an algebraic curve where the associated Cayley-Schreier graphs form an expander family exhibit strong forms of geometric... 
LAPLACIAN | EIGENVALUE | MATHEMATICS | ABELIAN-VARIETIES | RANDOM-WALKS | BOUNDS | EXPANSION | POINTS | CURVES | Mathematics - Number Theory | 14G05 | 05C50 | 35P15 | 05C40 | 14K15 | 14D10 | 14D05
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 2/2019, Volume 26, Issue 1, pp. 1 - 8
... Subject Classification. Primary 35P15, 35R11. Keywords. Fractional Laplacian, Anti-symmetry, Unit ball. 1. Introduction and main result Let d ≥ 1a n dD ⊂ R d... 
Unit ball | Analysis | 35R11 | Mathematics | Fractional Laplacian | Anti-symmetry | Primary 35P15 | MATHEMATICS, APPLIED
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 11/2017, Volume 89, Issue 3, pp. 377 - 408
We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint... 
Secondary 35P15 | 35B25 | Analysis | Dumbbell domains | Mathematics | 35J35 | Spectral analysis | Biharmonic operator | Primary 35J40 | MATHEMATICS | PERTURBATIONS | EIGENVALUE PROBLEMS | EQUILIBRIA | DYNAMICS | CONVERGENCE | SYSTEMS | ORDER ELLIPTIC-OPERATORS | PERTURBED DOMAINS
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 04/2017, Volume 95, Issue 2, pp. 500 - 518
We describe a highly efficient numerical scheme for finding two‐sided bounds for the eigenvalues of the fractional Laplace operator (−Δ)α/2 in the unit ball... 
35P15 | 35S05 | 65F15 (primary) | INTERVAL | MATHEMATICS | CAUCHY PROCESS | EQUATION | DOMAINS
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2019, Volume 51, Issue 1, pp. 49 - 69
We establish an explicit expression for the smallest non‐zero eigenvalue of the Laplace–Beltrami operator on every homogeneous metric on the 3‐sphere, or... 
22C05 | 58J53 | 58J50 (primary) | 35P15 | 53C30 (secondary) | MATHEMATICS | COMPACT | 1ST EIGENVALUE
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 02/2016, Volume 57, Issue 2, p. 23509
In the case of general compact quantum graphs, many-particle models with singular two-particle interactions were introduced by Bolte and Kerner [J. Phys. A:... 
CHAOS | STAR GRAPH | PHYSICS, MATHEMATICAL | QUANTUM GRAPHS | Particle interactions | Upper bounds | Eigenvectors
Journal Article
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2019, Volume 109, Issue 8, pp. 1805 - 1825
We analyze the ground state energy for N identical fermions in a two-dimensional box of volume L2 interacting with an external point scatterer. Since the point... 
Point interaction | Fermi polaron | Energy asymptotics | Thermodynamic limit | STABILITY | POINT | PHYSICS, MATHEMATICAL | Thermodynamics | Analysis
Journal Article
Archiv der Mathematik, ISSN 1420-8938, 2018, Volume 112, Issue 3, pp. 305 - 311
.... Primary 35P15; Secondary 35J05, 35J25, 35P20. Keywords. Dirichlet Laplacian, Eigenvalues, Faber–Krahn inequality, P´ olya’s conjecture. Let Ω be a bounded domain in R... 
Dirichlet Laplacian | Secondary 35J05 | Eigenvalues | Pólya’s conjecture | Mathematics, general | Mathematics | Faber–Krahn inequality | 35P20 | 35J25 | Primary 35P15 | MATHEMATICS | Polya's conjecture | Faber-Krahn inequality | DOMAINS
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2017, Volume 49, Issue 3, pp. 480 - 490
We give upper bounds on the principal Dirichlet eigenvalue associated to a smoothly bounded domain in a complete Riemannian manifold; the bounds involve... 
35P15 (primary) | 60J65 (secondary) | 58J65 | MATHEMATICS | DIFFUSIONS | 1ST DIRICHLET EIGENVALUE | INEQUALITY | EUCLIDEAN-SPACE | Mathematics - Spectral Theory
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2019, Volume 2019, Issue 1, pp. 90 - 139
We consider how the geometry and topology of a compact n-dimensional Riemannian orbifold with boundary relates to its Steklov spectrum. In two dimensions,... 
MATHEMATICS | EIGENVALUES | ISOSPECTRAL DEFORMATIONS | RICCI FLOW | INEQUALITIES | 2-ORBIFOLDS | LENS SPACES | METRICS | BOUNDARY | DOMAINS | RIEMANNIAN-MANIFOLDS
Journal Article
Complex variables and elliptic equations, ISSN 1747-6941, 2018, Volume 64, Issue 4, pp. 541 - 547
We provide an explicit upper bound of the eigenvalues corresponding to a weighted p-Laplacian operator defined on a connected metric graph with finite total... 
metric graph | p-Laplacian operator | Secondary: 34B45 | positive operator | Sobolev space | Primary: 35P15 | 46G12 | 41A30 | 81Q35 | 58J50 | 47B65 | 35R02 | MATHEMATICS | Eigenvalues | Upper bounds | Eigen values
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2017, Volume 145, Issue 5, pp. 2167 - 2181
As a corollary we obtain lower bounds for the individual eigenvalues \lambda _k, which for a certain range of k improves the Li-Yau inequality for convex... 
Berezin–Li–Yau inequality | Semi-classical estimates | Dirichlet-Laplace operator | semi-classical estimates | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDS | Berezin-Li-Yau inequality | DIRICHLET
Journal Article
Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 06/2019, Volume 27, Issue 2, pp. 179 - 211
We set out to obtain estimates of the Laplacian Spectrum of Riemannian manifolds with non-empty boundary. This was achieved using standard doubled manifold... 
Primary 35P15 53C20 | Secondary 53C21 58C40 | Regularized metric with control of curvature | Double of a manifold | Topological invariants | Laplacian | VIBRATION FREQUENCIES | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Annali di matematica pura ed applicata, ISSN 1618-1891, 2018, Volume 197, Issue 5, pp. 1511 - 1531
We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio “perimeter over area” among their own measurable subsets.... 
Weak regularity | 53A10 | Minimal Cheeger set | Capillarity | Mathematics, general | Cheeger problem | Mathematics | Secondary: 35P15 | Primary: 49Q10 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | PRESCRIBED MEAN-CURVATURE | EQUATION | Mathematics - Analysis of PDEs
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 08/2015, Volume 40, Issue 8, pp. 1467 - 1497
Given a selfadjoint, elliptic operator L, one would like to know how the spectrum changes as the spatial domain Ω ⊂ ℝ n is deformed. For a family of domains {Ω... 
Morse index | Secondary: 53D12 | Domain deformation | Elliptic boundary value problem | Maslov index | Primary: 35P15 | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRAL FLOW | Partial differential equations | Operators | Theorems | Spectral theory | Dirichlet problem | Boundary conditions | Boundaries | Subspaces
Journal Article
Communications in partial differential equations, ISSN 1532-4133, 2016, Volume 41, Issue 6, pp. 999 - 1028
In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a δ-interaction supported on a cone whose cross section... 
δ-interaction | existence of bound states | spectral asymptotics | Conical and hyperconical surfaces | Schrödinger operator | Primary: 35P20 | Secondary: 35P15, 35Q40, 35Q60, 35J10 | Operators | Axisymmetric | Thresholds | Partial differential equations | Eigenvalues | Schroedinger equation | Cross sections | Fibers | Mathematics | Spectral Theory
Journal Article
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