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math.AP2018
A Directional Lipschitz Extension Lemma, with Applications to Uniqueness and Lagrangianity for the Continuity Equation
Laura Caravenna, Gianluca Crippa
We prove a Lipschitz extension lemma in which the extension procedure simultaneously preserves the Lipschitz continuity for two non-equivalent distances. The two distances under co…
math.AP2018
On the structure of solutions for general hyperbolic systems of balance laws
Fabio Ancona, Laura Caravenna, Andrea Marson
The paper describes the qualitative structure of BV entropy solutions of a strictly hyperbolic system of balance laws with characteristic fields either piecewise genuinely nonlinea…
math.AP2015★ 2 cited
Schaeffer's regularity theorem for scalar conservation laws does not extend to systems
Laura Caravenna, Laura Spinolo
Schaeffer's regularity theorem for scalar conservation laws can be loosely speaking formulated as follows. Assume that the flux is uniformly convex, then for a generic smooth initi…