Théorème de décomposition de type Smirnov à partir des courbes ouvertes simples et régulières et étude de leurs propriétés

We present a new decomposition of two-dimensional divergence-measure vector fields into elementary measures supported on simple open curves, parametrized at constant speed.Our construction builds on Smirnov's decomposition theorem but is formulated in terms of parametrized curves of class $\mathrm{C}^3$, with constant speed; in particular, in the two-dimensional case, the non-constant curves are simple and open.The resulting structure facilitates the analysis of total variation measures and the study of their convergence, with potential applications in geometric measure theory and imaging.