The positive-definiteness of the Hamiltonian operator for Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. It was indeed well known that the Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from infinitely many inverse powers of the Laplacian. If space-time is replaced by a compact Riemannian four-manifold without boundary, on w...

Abstract The p -Laplacian for graphs, as well the vertex Laplace operator and hyperedge general setting of oriented hypergraphs, are generalized. In particular, both a defined all ? 1. Several spectral properties these operators investigated.

We prove a strong maximum principle for semicontinuous viscosity subsolutions or supersolutions of fully nonlinear degenerate elliptic PDE's, which complements the results of 17]. Our assumptions and conclusions are diierent from those in 17], in particular our maximum principle implies the nonexistence of a dead core. We test the assumptions on several examples involving the p-Laplacian and th...

A great deal of classical harmonic analysis is concerned with the properties of the Laplacian L on Euclidean space R and on the sphere Sn−1 in R . One of the key questions which inspired many of the experts on the subject was the following. Given a bounded Borel function m on R , we can define a bounded operator m(L) on L(R) using the functional calculus of self-adjoint operators on a Hilbert s...

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on RN . The Dunkl operators are denoted by Tj for 1 ≤ j ≤ N, and the Laplacian ∆κ = ∑j=1 T2 j . This paper finds the homogeneous harmonic polynomials annihilated by all Tj for j > 2. The structure constants with respect to the Gaussian and sphere inner...

The well-studied methods of current source density analysis use the Laplacian transform to identify locations and relative magnitudes of current sources and sinks. The method is typically used in reduced one-dimensional form for electrophysiological measures, due to technical limitations. The present paper outlines a two-dimensional method in which simultaneous samples are recorded from multipl...

We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when p 6= 2. We get around this difficulty by working with certain...

terracing is an operator that is applied to potential field data to produce regions of constant field amplitude that are separated by sharp boundaries. magnetic data are usually transformed into pseudo-gravity data (baranov, 1957) prior to the application of terracing. the objective of terracing is ‘to recast potential field maps into a geologic map like format’ (cordell and mccafferty 1989). t...

We show that the k-th eigenvalue of the Dirichlet Laplacian is strictly less than the k-th eigenvalue of the classical Stokes operator (equivalently, of the clamped buckling plate problem) for a bounded domain in the plane having a locally Lipschitz boundary. For a C boundary, we show that eigenvalues of the Stokes operator with Navier slip (friction) boundary conditions interpolate continuousl...