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<p>We prove an existence result for solutions to a class of nonlinear degenerate elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form associated to a family of vector fields which satisfy a Poincaré inequality and the doubling condition. Furthermore, we prove that the solutions satisfy a generalization of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> </InlineEquation>-regularity results which hold for the solutions to Leray–Lions type equations.</p>

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Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月14日

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  • Marco Picerni

摘要

We prove an existence result for solutions to a class of nonlinear degenerate elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form associated to a family of vector fields which satisfy a Poincaré inequality and the doubling condition. Furthermore, we prove that the solutions satisfy a generalization of the \(L^p\) -regularity results which hold for the solutions to Leray–Lions type equations.