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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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5 results for “bi-Laplacian”

Gelfand problem and Hemisphere rigiditymath.DG

The hemisphere rigidity theorem connects to the Gelfand problem, providing a precise value for the extremal parameter.

problem Finding the extremal parameter for a specific nonlinear equation on a hemisphere.

method Interpreting the hemisphere rigidity theorem within the context of the Gelfand problem and applying it to a fourth-order Gelfand problem.

result A precise value for the extremal parameter is derived for the Gelfand problem under certain conditions.

hemisphere rigidity Gelfand problem extremal parameter Q curvature bi-Laplacian

2021-02-20abs ↗pdf ↗

The biharmonic heat operator on edge manifolds and non-linear fourth order equationsmath.SP

We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping properties of the corresponding biharmonic heat operator on certain Banach spaces. Thi…

2013-01-30abs ↗pdf ↗

Estimates of eigenvalues of elliptical differential problems in divergence formmath.DG

The paper provides estimates for eigenvalues of elliptic differential problems.

problem Computing eigenvalue estimates for elliptic differential problems.

method Analytical computation of eigenvalues for specific types of elliptic differential equations.

result Universal estimates of eigenvalues and gaps between consecutive eigenvalues are derived.

eigenvalues elliptic differential equations divergence form gap between eigenvalues

2026-03-05abs ↗pdf ↗

Biharmonic functions and bi-eigenfunctions on some model spacesmath.DG

The paper studies biharmonic functions and bi-eigenfunctions on spheres and model spaces.

problem Characterizing biharmonic functions and eigenfunctions on model spaces.

method Analyzes bi-Laplacian on spheres, derives integral formulas for biharmonic solutions, and classifies proper biharmonic functions.

result Proper biharmonic functions on model spaces can be constructed from eigenfunctions of the factor sphere.

biharmonic functions model spaces spheres integral formulas eigenfunctions

2024-07-18abs ↗pdf ↗

Constant Q-curvature metrics with Delaunay ends: the nondegenerate casemath.DG

Constructs metrics with Q-curvature on manifolds with singularities.

problem Positive singular Q-curvature problem on compact manifolds with punctures.

method One-parameter family solutions, perturbation methods, gluing techniques, linearized operator mapping properties.

result One-parameter family of solutions constructed for positive Q-curvature.

Q-curvature positive curvature compact manifolds singularities perturbation methods

2021-10-11abs ↗pdf ↗