$LAPL laplacian

Latest papers

1. Learnable Hodge-Laplacian Driven Mixture of Experts for Steady-PDE Surrogates on Coarse Unstructured Meshes cs.LG · 14 Oct · 2 hits

   …experts, each focused on a different spectral scale. The partition is built from a discrete Hodge Laplacian $L_0=\star_0^{-1} d_0^{\top}\star_1 d_0$, that serves as a fitting layer measuring high-frequency…

2. Topological degree for singular $N$-mean field equations math.AP · 14 Oct · 1 hit

   …establish the sublevel homotopy equivalence. The arguments apply to the nonlinear, possibly degenerate $N$-Laplacian with singular weights, without requiring a global Palais--Smale condition or isolation and…

3. Emulating the Darcy Solution Operator by Heat-Semigroup Functional Calculus and Pointwise Products math.NA · 14 Oct · 1 hit

   …$A^{1+\theta}$, with an explicit rate attained by the scheme's product-defect block. The scheme unrolls the Laplacian-preconditioned Richardson iteration, controls each inexact step in the operator norm of $\dot H^1$…

4. A note on the failure of Payne's inequality on manifolds with boundary math.SP · 14 Oct · 1 hit

   We show that Payne's conjecture on the comparison between Dirichlet Laplacian eigenvalues and buckling eigenvalues does not hold on flat and hyperbolic cylindrical surfaces and on (round) hemispheres.

5. Resolvent Expansions at All Spectral Thresholds for Three-Dimensional Discrete Schr\"odinger Operators math.AP · 14 Oct · 1 hit

   …for the discrete Schr\"odinger operator $H=-\Delta+V $ on $\Z^3$, where $\Delta$ denotes the discrete Laplacian on $\mathbb{Z}^3$ and $V(n)$ is a real-valued decaying potential of $\mathbb{Z}^3$. At the…

6. Nearly sharp $W^{1,\infty}$ stability of polynomial spectral Ritz projections math.NA · 14 Oct · 1 hit

   …nearly sharp $W^{1,\infty}$ stability estimates for the Legendre spectral Ritz projection associated with Laplacian on a square domain. Its norm grows proportionally to the square root of the polynomial degree, up…

7. Heat Kernel Estimates for Random Walks with Killing on Transient Graphs math.PR · 13 Oct · 1 hit

   …graphs. The graphs we consider are transient and admit two-sided sub-Gaussian heat kernel estimates for the Laplacian $\Delta$, and the potentials $W$ decay to zero at infinity. We offer two proofs for one of our main…

8. Invariant factors from products of cyclotomic polynomials, with applications math.RA · 13 Oct · 1 hit

   …presented groups, homology groups of cyclic branched covers of knots, adjacency matrices and shifted graph Laplacians, $K$-theory, and Smith forms of matrix powers. For example, for two families of hyperbolic knots…