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<p>The exponential decay of entire solutions to elliptic equations has been extensively studied. In this paper, we introduce a new technique to prove sharp exponential decay for a wide range of elliptic operators. Our results are novel in two aspects. First, we treat partial differential inequalities, rather than restricting to equations. Second, the estimates apply to variable-coefficient problems and do not require rotational symmetry of solutions.</p>

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Exponential decay for elliptic equations

  • 期刊论文

  • 发表日期：

    2026年5月30日

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  • Hongyi Sheng,
  • Xu-Jia Wang,
  • Xinyue Zhang

摘要

The exponential decay of entire solutions to elliptic equations has been extensively studied. In this paper, we introduce a new technique to prove sharp exponential decay for a wide range of elliptic operators. Our results are novel in two aspects. First, we treat partial differential inequalities, rather than restricting to equations. Second, the estimates apply to variable-coefficient problems and do not require rotational symmetry of solutions.