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arXiv · 2512.24020

A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces

Jae-Hwan Choi·Junhee Ryu
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Abstract

We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and to the critical case of integer-order regularity. In addition, nonzero initial data are treated in the optimal trace space via a sharp trace theorem.

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Jae-Hwan Choi, Junhee Ryu. 2025-12-30. A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. https://arxiv.org/abs/2512.24020

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