A higher Dimensional Marcinkiewicz Exponent and the Riemann Boundary Value Problems for Polymonogenic Functions on Fractals Domains

2023/07/27 by Castro, Carlos Daniel Tamayo, Reyes, Juan Bory
#28A80 #30G30 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30G35 #Secondary 30E20

paper · doi:10.48550/arxiv.2307.14560

Abstract

We use a high-dimensional version of the Marcinkiewicz exponent, a metric characteristic for non-rectifiable plane curves, to present a direct application to the solution of some kind of Riemann boundary value problems on fractal domains of Euclidean space ℝⁿ⁺¹, n≥2 for Clifford algebra-valued polymonogenic functions with boundary data in classes of higher order Lipschitz functions. Sufficient conditions to guarantee the existence and uniqueness of solution to the problems are proved. To illustrate the delicate nature of this theory we described a class of hypersurfaces where the results are more refined than those that exist in literature.

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