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Vectorial Kato inequality for 𝑝-harmonic maps with optimal constant

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This work derives the sharp Kato inequality for p-harmonic functions, enhancing the study of regularity in mappings.

The derived vectorial Kato inequality reveals a new optimal constant for p-harmonic mappings.
It shows that regularity is achieved for p values between 2 and 2.642 in specific mappings.
Applications include advancing the understanding of regularity conditions in p-harmonic maps.
This inequality highlights a distinct difference from previously established constants for scalar p-harmonic functions.

Gastel et al. (2025) studied this question.

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