Hölder regularity of continuous solutions to balance laws and applications in the Heisenberg group

Laura Caravenna, Elio Marconi, Andrea Pinamonti

We prove Hölder regularity of any continuous solution $u$ to a $1$-D scalar balance law $u_t+[f(u){]}_x=g$, when the source term $g$ is bounded and the flux $f$ is nonlinear of o…