EXISTENCE OF STRONG TRACES FOR QUASI-SOLUTIONS OF MULTIDIMENSIONAL CONSERVATION LAWS

Abstract

We consider a conservation law in the domain Ω ⊂ ℝ n+1 with C 1 boundary ∂Ω. For a wide class of functions including generalized entropy sub- and super-solutions, we prove the existence of strong traces for normal components of the entropy fluxes on ∂Ω. Non-degeneracy conditions on the flux are not required.