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 variational characterization of condenser capacities in within a class of plurisubharmonic 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.
Adams inequality on metric measure spaces.
Admissible functions for the Dirichlet space
Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of .
Alexander's capacity for intersections of ellipsoids in .
Alexander’s projective capacity for polydisks and ellipsoids in
Alexander’s projective capacity for the polydisk and the ellipsoid in is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in is proved to have an asymptotic behaviour in similar to that of the Siciak homogeneous extremal function associated with K.
Allied integrals, functions, and series for the unit sphere.
Allure des potentiels a la frontière et fonctions fortement sousharmoniques
Almansi decompositions for polyharmonic, polyheat, and polywave functions
We construct Almansi decompositions for a class of differential operators, which include powers of the classical Laplace operator, heat operator, and wave operator. The decomposition is given in a constructive way.
An application of Bergmann-Whittaker operator.
An application of Bergman-Whittaker operator
An application of subordination on harmonic function.
An Approximation Theorem for Integrable Harmonic Vector Fields.
An asymptotic expansion for the discrete harmonic potential.
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 energy estimate for the complex Monge-Ampère operator
We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.