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<p>We establish Liouville type results for weighted anisotropic elliptic equations in divergence form in the strip <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {R}}^{N-1}\times (-1,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The weights depend on one variable and they include the case where they are powers of the distance functions to the boundary of the strip.</p>

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Liouville type properties for a class of weighted anisotropic elliptic equations

  • 期刊论文

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  • 发表日期：

    2025年9月22日

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  • Stathis Filippas,
  • Luisa Moschini,
  • Achilles Tertikas

摘要

We establish Liouville type results for weighted anisotropic elliptic equations in divergence form in the strip \({\mathbb {R}}^{N-1}\times (-1,1)\) R N - 1 × ( - 1 , 1 ) , \(N\ge 2\) N ≥ 2 . The weights depend on one variable and they include the case where they are powers of the distance functions to the boundary of the strip.