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arXiv · 1208.3959

On the Hamilton-Jacobi Equation and Infimal Convolution in the Framework of Sobolev-functions

Hannes Luiro
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Abstract

We study the regularity properties of the Hamilton-Jacobi flow equation and infimal convolution in the case where initial datum function is continuous and lies in given Sobolev-space $W^{1,p}(\rn)$. We prove that under suitable assumptions it holds for solutions $w(x,t)$ that $D_xw(\cdot,t)\to Du(\cdot)$ in $L^p(\rn)$. Moreover, we construct examples showing that our results are essentially optimal.

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Hannes Luiro. 2012-08-20. On the Hamilton-Jacobi Equation and Infimal Convolution in the Framework of Sobolev-functions. https://arxiv.org/abs/1208.3959

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