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arXiv · 1909.12197

Tent space well-posedness for parabolic Cauchy problems with rough coefficients

Wiktoria Zatoń
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Abstract

We study the well-posedness of Cauchy problems on the upper half space $\mathbb{R}^{n+1}_+$ associated to higher order systems $\partial_t u =(-1)^{m+1}\mbox{div}_m A\nabla ^m u$ with bounded measurable and uniformly elliptic coefficients. We address initial data lying in $L^p$ ($1 2$, what is also new for the case $m>1$.

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Wiktoria Zatoń. 2019-09-26. Tent space well-posedness for parabolic Cauchy problems with rough coefficients. https://doi.org/10.1016/j.jde.2020.07.033

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