The \( p \)-Laplacian is a nonlinear generalization of the classical Laplace operator, typically denoted as \( \Delta_p \). It is used extensively in the study of partial differential equations (PDEs) and variational problems.
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The p-Laplacian is the nonlinear divergence-form operatorIt is the Euler-Lagrange operator of the p-energy. For it is degenerately elliptic where .