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arXiv · 2208.10277

Marcinkiewicz Exponent and Boundary Value Problems in Fractal Domains of $\mathbb{R}^{n+1}$

Carlos Daniel Tamayo Castro
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Abstract

This paper aims to study the jump problem for monogenic functions in fractal hypersurfaces of Euclidean spaces. The notion of the Marcinkiewicz exponent has been taken into consideration. A new solvability condition is obtained, basing the work on specific properties of the Teodorescu transform in Clifford analysis. It is shown that this condition improves those involving the Minkowski dimension.

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Carlos Daniel Tamayo Castro. 2022-08-14. Marcinkiewicz Exponent and Boundary Value Problems in Fractal Domains of $\mathbb{R}^{n+1}$. https://arxiv.org/abs/2208.10277

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