# Sbv regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function

## Summary (1 min read)

### Summary

- In this work the authors study the regularity of entropy solutions of the genuinely nonlinear scalar balance laws SBV regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function.
- In their proofs the authors will have to deal with one-dimensional fun tions of bounded variation, therefore they olle t here some useful properties.
- The authors shall make use of these Theorems and in parti ular of the Norossing property of Theorem 3.3, to prove the SBVloc regularity of u(x, t).
- In here the authors state the Theorem for genuine hara teristi be ause under an appropriate normalization, the notions of "sho k-free" and "genuine" are equivalent.
- Two genuine hara teristi s may interse t only at their end points.
- In this part of the paper the authors analyze the regularity of the entropy solutions of the onservation laws (1).
- Moreover, u has a better stru ture than any 2-dimensional BV -fun tion.

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### "Sbv regularity of entropy solutions..." refers background in this paper

...Scalar conservation laws in one space dimension and Hamilton–Jacobi equations in one dimension are strictly connected: entropy solutions correspond to viscosity solutions (see [9])....

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### "Sbv regularity of entropy solutions..." refers background or methods in this paper

...This change of strategy is also motivated by the fact that for system of conservation laws the Hopf–Lax does not exists, whereas there is a suitable concept of generalized characteristics (see [8])....

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...Moreover, we will restrict our analysis on good representative of solutions and then, under our initial hypothesis we follow the works of Dafermos [6–8] giving an introduction to the theory of generalized characteristics and recalling here some results, which we shall use in the sequel....

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...Fortunately, we can make use of the theory of generalized characteristics introduced by Dafermos (see [6–8]) to analyze the behavior of the characteristics for entropy solutions of (1....

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...In [8], the generalized characteristic of Theorem 3....

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