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A degenerate elliptic operator has a positive semidefinite principal form that may lose positive definiteness at some points or jets. The <p-Laplacian> with $p>2$ degenerates where its solution has zero gradient.

= Degenerate ellipticity
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Degenerate elliptic operator

{c}
{title2=$\Delta_pu=\operatorname{div}(|Du|^{p-2}Du)$}
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The p-Laplacian is the nonlinear divergence-form operator
$$
\Delta_pu=\operatorname{div}(|Du|^{p-2}Du).
$$
It is the <Euler-Lagrange equation>[Euler-Lagrange operator] of the <p-energy>. For $p>2$ it is <degenerate ellipticity>[degenerately elliptic] where $Du=0$.

= p-Laplacian equation
{c}
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 Incoming links: p-Laplacian