What question did this study set out to answer?

The aim is to establish local Hölder regularity for weak solutions of nonlocal diffusion equations.

Local Hölder regularity for nonlocal porous media and fast diffusion equations with general kernel

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The aim is to establish local Hölder regularity for weak solutions of nonlocal diffusion equations.
Analysis of locally bounded, weak solutions of the fractional porous media equations
Utilization of De Giorgi-Nash-Moser theory
Study of singularity and degeneracy sets influenced by the solution's geometry
Locally bounded solutions are demonstrated to be locally Hölder continuous
Establishment of new regularity results even for solutions with constant coefficients
Analysis extends existing knowledge to a broader class of nonlocal equations

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Analysis shows local Hölder continuity in nonlocal diffusion equations, indicating new insights into their behavior.

Kim et al. (2026) studied this question.

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