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This is a Quantitative Study study.

October 3, 2025Open Access

A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces

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Authors

JCJae-Hwan ChoiKorea Institute for Advanced Study JKJae-Hoon KangSeoul National University DPDaehan ParkKorea Institute for Advanced Study

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Implication

This article demonstrates existence and uniqueness of solutions to time-fractional equations involving non-local operators in Sobolev spaces, highlighting the use of probabilistic methods.

Key Points

Solutions to time-fractional evolution equations exist uniquely in Sobolev spaces, and estimates are established.
The anisotropic non-local operators are derived from subordinate Brownian motions, affecting the solution's regularity.
Traditional Fourier analysis methods are limited due to singularities in operator transforms, necessitating a probabilistic approach.
Generalized real interpolation theory is used to identify optimal initial data space for the solutions.

Cite This Study

Choi et al. (2025) studied this question.

synapsesocial.com/papers/68e03501f0e39f13e7fa39b0 https://doi.org/10.48550/arxiv.2505.00984

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Implication

This article demonstrates existence and uniqueness of solutions to time-fractional equations involving non-local operators in Sobolev spaces, highlighting the use of probabilistic methods.

A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces

Discussion

Member takes

Implication

Key Points

Cite This Study

A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces

Discussion

Member takes

Implication

Key Points

Cite This Study

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