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<p>We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2<i>s</i> which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(o(|x|^{-(N+2s)})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>o</mi> <mo stretchy="false">(</mo> <mo stretchy="false">|</mo> <mi>x</mi> <msup> <mo stretchy="false">|</mo> <mrow> <mo>-</mo> <mo stretchy="false">(</mo> <mi>N</mi> <mo>+</mo> <mn>2</mn> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> at infinity. Our result is new even in the case of the fractional Laplacian in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation>, as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial.</p>

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The Landis conjecture for nonlocal elliptic operators: polynomial decay

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Sebastián Flores Sepúlveda,
  • Gabrielle Nornberg

摘要

We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption \(o(|x|^{-(N+2s)})\) o ( | x | - ( N + 2 s ) ) at infinity. Our result is new even in the case of the fractional Laplacian in \(\mathbb {R}^N\) R N , as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial.