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<p>In this paper, we establish the properties of viscosity solutions in Martinet spaces, which are sub-Riemannian spaces that lack both the algebraic group law of Carnot groups and the triangular vector fields of Grushin-type spaces. We then prove the uniqueness of viscosity solutions to strictly monotone elliptic PDEs, to the infinite Laplace equation, and to the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbf {\infty (x)}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∞</mi> <mo stretchy="false">(</mo> <mi mathvariant="bold">x</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplace equation.</p>

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Viscosity solutions in Martinet spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Thomas Bieske,
  • Frederic Bowen

摘要

In this paper, we establish the properties of viscosity solutions in Martinet spaces, which are sub-Riemannian spaces that lack both the algebraic group law of Carnot groups and the triangular vector fields of Grushin-type spaces. We then prove the uniqueness of viscosity solutions to strictly monotone elliptic PDEs, to the infinite Laplace equation, and to the \({\mathbf {\infty (x)}}\) ∞ ( x ) -Laplace equation.