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Biharmonic morphisms

Mustapha ChadliMohamed El KadiriSabah Haddad — 2005

Commentationes Mathematicae Universitatis Carolinae

Let ( X , ) and ( X ' , ' ) be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from ( X , ) to ( X ' , ' ) is a continuous map from X to X ' which preserves the biharmonic structures of X and X ' . In the present work we study this notion and characterize in some cases the biharmonic morphisms between X and X ' in terms of harmonic morphisms between the harmonic spaces associated with ( X , ) and ( X ' , ' ) and the coupling kernels of them.

On the integral representation of finely superharmonic functions

Abderrahim AslimaniImad El GhaziMohamed El Kadiri — 2019

Commentationes Mathematicae Universitatis Carolinae

In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset U of a Brelot 𝒫 -harmonic space Ω with countable base of open subsets and satisfying the axiom D . When Ω satisfies the hypothesis of uniqueness, we define the Martin boundary of U and the Martin kernel K and we obtain the integral representation of invariant functions by using the kernel K . As an application of the integral representation we extend to the cone 𝒮 ( 𝒰 ) of nonnegative...

On the potential theory of some systems of coupled PDEs

Abderrahim AslimaniImad El GhaziMohamed El KadiriSabah Haddad — 2016

Commentationes Mathematicae Universitatis Carolinae

In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type L 1 u = - μ 1 v , L 2 v = - μ 2 u , on a domain D of d , where μ 1 and μ 2 are suitable measures on D , and L 1 , L 2 are two second order linear differential elliptic operators on D with coefficients of class 𝒞 . We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with L 1 and L 2 , and a convergence...

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