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arXiv · 2307.01654

Calder\'on-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients

Sun-Sig Byun·Kyeongbae Kim·Deepak Kumar
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Abstract

We prove Calder\'on-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of fractional Laplacian type data and a non-divergence type data. Interestingly, even though the kernel coefficients are discontinuous, we obtain a significant increment of fractional differentiability for the solutions, which is not observed in the corresponding local parabolic equations.

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Sun-Sig Byun, Kyeongbae Kim, Deepak Kumar. 2023-07-04. Calder\'on-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients. https://arxiv.org/abs/2307.01654

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