A biharmonic elliptic problem with dependence on the gradient and the Laplacian.
A class of functions containing polyharmonic functions in ℝⁿ
Some properties of the functions of the form in ℝⁿ, n ≥ 2, where each is a harmonic function defined outside a compact set, are obtained using the harmonic measures.
A maximum principle for biharmonic functions in Lipschitz and C1 domains.
A polyharmonic analogue of a Lelong theorem and polyhedric harmonicity cells.
A Proof of the Hardy-Littlewood Theorem on Fractional Integration and a Generalization
A Quadratic Finite Element Method for solving Biharmonic Problems in IRn.
A regularity result for polyharmonic variational inequalities with thin obstacles
A uniqueness theorem for higher order elliptic partial differential equations.
An infinite-harmonic analogue of a Lelong theorem and infinite-harmonicity cells.
Applications polynomiales et applications entières dans les espaces vectoriels topologiques
Axiomatique des fonctions biharmoniques. I
Les théories axiomatiques existantes de fonctions harmoniques ne s’appliquent pas à des équations simples d’ordre , comme l’équation biharmonique ou le système équivalent , .On développe donc ici, au moyen d’un faisceau de couples convenables de fonctions une approche axiomatique locale applicable à des équations du type , où () est un opérateur linéaire du second ordre elliptique ou parabolique. Deux axiomatiques harmoniques lui sont associées. On traite, dans ce cadre, le problème (généralisé)...
Behavior of biharmonic functions on Wiener's and Royden's compactifications
Let be a smooth Riemannian manifold of finite volume, its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of are found, and for biharmonic functions (those for which ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.
Biharmonic Green domains in a Riemannian manifold
Let be a Riemannian manifold without a biharmonic Green function defined on it and a domain in . A necessary and sufficient condition is given for the existence of a biharmonic Green function on .
Biharmonic Green's functions and biharmonic degeneracy.
Biharmonic Green's Functions and Quasiharmonic Degeneracy.
Biharmonic morphisms
Let and be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from to is a continuous map from to which preserves the biharmonic structures of and . In the present work we study this notion and characterize in some cases the biharmonic morphisms between and in terms of harmonic morphisms between the harmonic spaces associated with and and the coupling kernels of them.
Boundary Minimum Principles in Potential Theory.
approximations of convex, subharmonic, and plurisubharmonic functions
Completeness and existence of bounded biharmonic functions on a riemannian manifold
A.S. Galbraith has communicated to us the following intriguing problem: does the completeness of a manifold imply, or is it implied by, the emptiness of the class of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry -functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension that carry...
Decomposition of polyharmonic functions with respect to the complex Dunkl Laplacian.