Related papers: Harmonic functions on balls for x-dependent rectil…
This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly compact and without boundary). We discuss both local results obtained by analyzing eigenfunctions on small balls, and global results obtained by wave…
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
We give a proof that the first eigenfunction of the $\alpha$-symmetric stable process on a bounded Lipschitz domain in $\R^d$, $d\geq 1$, is superharmonic for $\alpha=2/m$, where $m>2$ is an integer. This result was first proved for the…
We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared…
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…
We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their…
In this article we are interested in finding positive discrete harmonic functions with Dirichlet conditions in three quadrants. Whereas planar lattice (random) walks in the quadrant have been well studied, the case of walks avoiding a…
We show that elliptic Harnack inequality is stable under form-bounded perturbations for strongly local Dirichlet forms on complete locally compact separable metric spaces that satisfy metric doubling property (or equivalently, relative ball…
We study the growth rate of harmonic functions in two aspects: gradient estimate and frequency. We obtain the sharp gradient estimate of positive harmonic function in geodesic ball of complete surface with nonnegative curvature. On complete…
Using known mode properties, the functional determinant for massless spin-half fields on the Euclidean 4-ball is calculated and shown to be different for spectral (nonlocal) and mixed (local) boundary conditions. The local result agrees…
We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes…
We consider the nonlinear wave equation, with a large exponent, power-like non-linearity, outside a ball of the Euclidean 3-dimensional space. In a previous article, we have proved that any global solution converges, up to a radiation term,…
In this work, we investigate some connections between exact differential equations and harmonic functions and in particular, we obtain necessary and sufficient conditions for which exact equations admit harmonic solutions. As an…
Formulae for the value of a harmonic function at the center of a rectangle are found that involve boundary integrals. The central value of a harmonic function is shown to be well approximated by the mean value of the function on the…
The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the…
We study the growth of harmonic functions on complete Riemann-ian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kazue. We also get a Cheng and Yau estimates for the…
The subject of this paper is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desired features of a spectral method, which is defined by a…
Using symmetrization techniques, we show that, for every $N \geq 2$, any second eigenfunction of the fractional Laplacian in the $N$-dimensional unit ball with homogeneous Dirichlet conditions is nonradial, and hence its nodal set is an…
The set of infinite-dimensional, symmetric stable tail dependence functions associated with exchangeable max-stable sequences of random variables with unit Fr\'echet margins is shown to be a simplex. Except for a single element, the…
We give solutions to some extremal problems involving distance function in mixed norm spaces of harmonic functions on the unit ball of R^n