Marcinkiewicz Exponent and Boundary Value Problems in Fractal Domains of ℝⁿ⁺¹

2022/08/14 by Carlos Daniel Tamayo Castro, Castro, Carlos Daniel Tamayo
Mathematics · #Algebraic and Geometric Analysis #advanced mathematical theories #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2208.10277

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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