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Majorantes surharmoniques minimales d'une fonction continue

Abstract : Let Ω be an open subset of R n and f:Ω→R a continuous function. A superharmonic majorant of f in Ω is called minimal if it is harmonic in the (open) set where if differs from f. Many properties of these functions are similar to those of nonnegative harmonic functions in Ω (in fact the case f=0); e.g. the whole family is uniformly equicontinuous in each compact subset of Ω, with respect to the uniform structure of R ‾. Application is made to the “Dirichlet” problem of finding a minimal superharmonic majorant of f agreeing with given boundary values (a problem arising from the mechanics of continua and formerly studied by hilbertian methods).
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Jean Jacques Moreau. Majorantes surharmoniques minimales d'une fonction continue. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 1971, 21 (2), pp.129 - 156. ⟨10.5802/aif.375⟩. ⟨hal-01788488⟩

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