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<p>In this work, we make use of the Almgren frequency function to establish a unique continuation property for the solutions of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( B_p \)</EquationSource> </InlineEquation>-Laplace equation given by <Equation ID="Equ17"> <EquationSource Format="TEX">\(\begin{aligned} B_p:=\operatorname {div}(B(x)|\nabla v|^{p-2}\nabla v) = 0 \quad \text {in } \Omega , \end{aligned}\)</EquationSource> </Equation>where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \Omega \)</EquationSource> </InlineEquation> is an open connected subset of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( \mathbb {R}^n \)</EquationSource> </InlineEquation>, with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( n \ge 2 \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\( 2 \le p &lt; \infty \)</EquationSource> </InlineEquation> and where <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( B(x) \)</EquationSource> </InlineEquation> is a symmetric <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\( n \times n \)</EquationSource> </InlineEquation> matrix-valued function on <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\( \Omega \)</EquationSource> </InlineEquation>.</p>

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The weak unique continuation for the p-Laplacian equation with weight

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Hajar El Ballout,
  • Omar Chakrone,
  • Mohammed Chehabi

摘要

In this work, we make use of the Almgren frequency function to establish a unique continuation property for the solutions of the \( B_p \) -Laplace equation given by \(\begin{aligned} B_p:=\operatorname {div}(B(x)|\nabla v|^{p-2}\nabla v) = 0 \quad \text {in } \Omega , \end{aligned}\) where \( \Omega \) is an open connected subset of \( \mathbb {R}^n \) , with \( n \ge 2 \) and \( 2 \le p < \infty \) and where \( B(x) \) is a symmetric \( n \times n \) matrix-valued function on \( \Omega \) .