On generalized Dirichlet integrals in the smooth and in the o-minimal setting

Gian Maria Dall'Ara

Given a compact manifold $M$ equipped with smooth vector fields $X_1,\dots ,X_r$, we consider the generalized Dirichlet energy \[\mathbf{E}(f)= \sum_{j=1}^r\int_M |X_jf|^2\, dm,\]…