Generalized coarea formula and fractal sets

Abstract

For any domain ω of R N (N≥1), the classGC (ω) of functionals Λ:L 1 (ω) → [0, +∞] fulfilling the followinggeneralized coarea formula is introduced: The main properties of this class of functionals are here investigated.\gL r and $$\tilde \Lambda _r $$ also allow us to construct two new definitions offractional dimension for set boundaries. Applications to models ofsurface tension effects in two-phase systems are then outlined. In particular,\gL r and $$\tilde \Lambda _r $$ allow us to represent very irregular phase interfaces.