Weyl's lemma states that every weak solution of Laplace's equation is also a smooth solution. We find that there is no Weyl's lemma for 2-Hessian equations. For any α small, we construct infinitely many C^ (1,α) very weak solutions ...
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Plan of the course: Part 1. Deterministic scalar conservation laws: The example of the Burgers equation and the non-existence of a global smooth solution. Definition of weak solution. Non-uniqueness. The concept of entropy solution. Young measur...
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