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In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_{1}u=-{\mu }_{1}v$, $L_{2}v=-{\mu }_{2}u$, on a domain $D$ of ${ℝ}^d$, where ${\mu }_1$ and ${\mu }_2$ are suitable measures on $D$, and $L_1$, $L_2$ are two second order linear differential elliptic operators on $D$ with coefficients of class ${𝒞}^{\infty }$. 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...

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