A higher dimensional Marcinkiewicz Exponent and the Riemann Boundary Value Problems for Polymonogenic Functions on Fractals Domains
Journal of Mathematical Analysis and Applications(2024)
摘要
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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关键词
Clifford analysis,Riemann boundary value problem,polymonogenic functions,fractal boundaries
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