Deformation from symmetry for Schrödinger equations of higher order on unbounded domains.
Dirichlet finite biharmonic functions on the Poincaré N-ball.
Dirichlet Finite Biharmonic Functions with Dirichlet Finite Laplacians.
Distributions bi-sousharmoniques sur
L’object de ce travail est l’etude des fonctions fonctions localement sommable sur , vérifiant (où est Laplacien pris au sens des distributions) et que se comportent à l’infini comme des fonctions sousharmoniques. En parculier, nous caractérisons les fonctious qui sont à la fois bi-sousharmoniques et sousharmoniques.
Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions
Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions are given. These proofs are on the calculus level and use only the basic knowledge of harmonic functions given in Axler, Bourdon and Ramey's book.
Existence of solutions for a family of polyharmonic and biharmonic equations.
Fonctions biharmoniques adjointes
The study of the equation (L₂L₁)*h = 0 or of the equivalent system L*₂h₂ = -h₁, L*₁h₁ = 0, where is a second order elliptic differential operator, leads us to the following general framework: Starting from a biharmonic space, for example the space of solutions (u₁,u₂) of the system L₁u₁ = -u₂, L₂u₂ = 0, being elliptic or parabolic, and by means of its Green pairs, we construct the associated adjoint biharmonic space which is in duality with the initial one.
Generators of the Space of Bounded Biharmonic Functions.
Harmonic and polyharmonic degeneracy.
Harnack's properties of biharmonic functions
Study of the equicontinuity of biharmonic functions, of the Harnack's principle and inequalities, and of their relations.
Iterated integral operators in Clifford analysis.
Liouville's theorem and the restricted mean property for biharmonic functions.
Manifolds carrying bounded quasiharmonic but no bounded harmonic functions.
Martin boundary associated with a system of PDE
In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e. ) and for non negative solutions of the equation .
Multivariate smooth interpolation that employs polyharmonic functions
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example...
On certain oscillatory properties for solutions of an equation with a biharmonic leading part
On certain reflexion principes
On duality and interpolation for spaces of polyharmonic functions
On extensions of the Mittag-Leffler theorem
The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
On Hadamard's problem for higher dimensions.