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arXiv · 2412.21014

Regularity results for elliptic and parabolic systems of partial differential equations

Luciana Angluli·Simone Ferrari·Luca Lorenzi
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Abstract

We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the space of bounded and continuous functions over $\R^d$. Consequently, we deduce relevant regularity results both in H\"older and Zygmund spaces and in Sobolev and Besov spaces.

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Luciana Angluli, Simone Ferrari, Luca Lorenzi. 2024-12-30. Regularity results for elliptic and parabolic systems of partial differential equations. https://arxiv.org/abs/2412.21014

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