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<p><i>It is known that a function with bounded variation can be represented as an at most countable sum of monotone parts. We show that if such a function belongs to a Sobolev space then the gradients of its monotone components have disjoint supports.</i></p>

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DECOMPOSITION OF WEAKLY DIFFERENTIABLE FUNCTIONS INTO MONOTONE PARTS

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • N. A. Gusev,
  • M. V. Korobkov

摘要

It is known that a function with bounded variation can be represented as an at most countable sum of monotone parts. We show that if such a function belongs to a Sobolev space then the gradients of its monotone components have disjoint supports.