2024/09/09 by Fabio Ancona, Ancona, Fabio, Laura Caravenna +3
Economics, Econometrics and Finance · Mathematics · #35L45 #35L65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.2409.06095
openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we discuss the SBV-regularity for a scalar balance law in one space dimension as a case study in order to explain the strategy that we apply in a separate paper to general hyperbolic systems of balance laws in one space dimension. While for a single balance law the more general work by Robyr is already available, the case of 1d-systems presents new behaviors that require a different strategy. This is why in this note we make the effort to introduce the notation and tools that are required for the case of more equations. When the flux presents linear degeneracies, it is know that entropy solutions can present nasty fractal Cantor-like behaviors, although f'(u) is still SBV: we thus discuss SBV-like regularity generalizing the work by Bianchini-Yu as SBV-regularity fails.