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<p>Necessary and sufficient conditions have been found for the existence of an extension across a smooth curve for the gradients of functions defined and biharmonic in the corresponding domains adjacent to the given curve. Moreover, the found extension determines the gradient of the biharmonic function in the union of the indicated domains and has continuous partial derivatives of certain orders at the curve’s points.</p>

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Piecewise biharmonic extension of gradients and monogenic functions

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Serhii V. Gryshchuk

摘要

Necessary and sufficient conditions have been found for the existence of an extension across a smooth curve for the gradients of functions defined and biharmonic in the corresponding domains adjacent to the given curve. Moreover, the found extension determines the gradient of the biharmonic function in the union of the indicated domains and has continuous partial derivatives of certain orders at the curve’s points.