On the instability of Hausdorff content.
On the integral representation of finely superharmonic functions
In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset of a Brelot -harmonic space with countable base of open subsets and satisfying the axiom . When satisfies the hypothesis of uniqueness, we define the Martin boundary of and the Martin kernel and we obtain the integral representation of invariant functions by using the kernel . As an application of the integral representation we extend to the cone of nonnegative...
On the integral representation of superbiharmonic functions
We consider a nonnegative superbiharmonic function satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions satisfying the condition in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman...
On the Iversen-Tsuji theorem quasiregular mappings.
On the Legendre and Laplace transformations
On the limits of the potential of the double distribution (Preliminary communication)
On the Liouville property for sublaplacians
On the logarithmic potential
On the logarithmic potential defined for a Van Koch curve.
On the logarithmic potential of the double distribution
On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
The Martin compactification of a bounded Lipschitz domain is shown to be for a large class of uniformly elliptic second order partial differential operators on .Let be an open Riemannian manifold and let be open relatively compact, connected, with Lipschitz boundary. Then is the Martin compactification of associated with the restriction to of the Laplace-Beltrami operator on . Consequently an open Riemannian manifold has at most one compactification which is a compact Riemannian...
On the mean value property of finely harmonic and finely hyperharmonic functions.
On the mean value property of superharmonic and subharmonic functions.
On the mean-value property of superharmonic functions
We complement a previous result concerning a converse of the mean-value property for smooth superharmonic functions. The case of harmonic functions was treated by Kuran and an improvement was given by Armitage and Goldstein.
On the modified logarithmic potential
On the multivariate transfinite diameter
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
On the Neumann operator of the arithmetical mean.
On the Neumann Problem for the Nonlinear Parabolic Equation of Eells-Sampson and Harmonie Mappings.
On the numerical solution of the first biharmonic equation
On the optimal growth of functions with bounded Laplacian.