A Theory of Capacities for Potentials of Functions in Lebesgue Classes.
A uniform boundary Harnack inequality on non-tangentially accessible domains.
A uniqueness theorem for higher order elliptic partial differential equations.
A uniqueness theorem for invariantly harmonic functions in the unit ball of Cn.
We prove a boundary uniqueness theorem for harmonic functions with respect to Bergman metric in the unit ball of Cn and give an application to a Runge type approximation theorem for such functions.
A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions
Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate . As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.
Abbildungen harmonischer Raüme mit Anwendung auf die Laplace und Wärmeleitungsgleichung
This paper is devoted to a study of harmonic mappings of a harmonic space on a harmonic space which are related to a family of harmonic mappings of into . In this way balayage in may be reduced to balayage in . In particular, a subset of is polar if and only if is polar. Similar result for thinness. These considerations are applied to the heat equation and the Laplace equation.
About mathematical model or some diffuse processes in the Mediterranean and exterior Poincare problem for the Helmholtz equation.
Allied integrals, functions, and series for the unit sphere.
An application of Bergmann-Whittaker operator.
An application of Bergman-Whittaker operator
An Approximation Theorem for Integrable Harmonic Vector Fields.
An elliptic semilinear equation with source term involving boundary measures: the subcritical case.
We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2),⎧ Δu + uq = 0, in Ω⎨⎩ u = μ, on ∂Ωwhere 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted Marcinkiewicz spaces.
An example concerning the topological character of the zero-set of a harmonic function.
An example related to boundedness of subharmonic functions
An extension theorem for supertemperatures.
An generalization of the Riesz potential
An infinite-harmonic analogue of a Lelong theorem and infinite-harmonicity cells.
An integral inequality for capacities.
An inversion formula and a note on the Riesz kernel
For potentials , where and are certain Schwartz distributions, an inversion formula for is derived. Convolutions and Fourier transforms of distributions in -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order , , of a compact subset of has the following property: its restriction to the interior of is an absolutely continuous measure with analytic density which is expressed by an explicit formula.
An operator connected with the third boundary value problem in potential theory