# On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations

Abstract : We give a simplified proof of regularizing effects for first-order Hamilton-Jacobi Equations of the form $u_t+H(x,t,Du)=0$ in $\R^N\times(0,+\infty)$ in the case where the idea is to first estimate $u_t$. As a consequence, we have a Lipschitz regularity in space and time for coercive Hamiltonians and, for hypo-elliptic Hamiltonians, we also have an H\"older regularizing effect in space following a result of L. C. Evans and M. R. James.
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https://hal.archives-ouvertes.fr/hal-01214425
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Submitted on : Monday, October 12, 2015 - 11:38:01 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM
Long-term archiving on: : Wednesday, January 13, 2016 - 11:34:32 AM

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reg_effect-fin.pdf
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### Identifiers

• HAL Id : hal-01214425, version 1
• ARXIV : 1510.03207

### Citation

Guy Barles, Emmanuel Chasseigne. On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations. 2015. ⟨hal-01214425⟩

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