We show a convergence property of certain families of finely harmonic functions in a fine domain U of ℝⁿ (n ≥ 2). We apply it to establish a certain regularity of the fine Green kernel of U.
We give a characterization of functions that are uniformly approximable on a compact subset of by biharmonic functions in neighborhoods of .
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.
In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset of a Brelot -harmonic space with countable base of open subsets and satisfying the axiom . When satisfies the hypothesis of uniqueness, we define the Martin boundary of and the Martin kernel and we obtain the integral representation of invariant functions by using the kernel . As an application of the integral representation we extend to the cone of nonnegative...
In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type , , on a domain of , where and are suitable measures on , and , are two second order linear differential elliptic operators on with coefficients of class . 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 and , and a convergence...
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