<span title="Home" class="fa-solid-900 icon"></span> Home

Codex Wiki

Mathematics

Area of mathematics

Analysis

Partial differential equation

Quasilinear partial differential equation

{c}
{title2=$\Delta_pu=\operatorname{div}(|Du|^{p-2}Du)$}
{wiki}

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}
{synonym}


p-Laplacian

Degenerate elliptic operator

{wiki=P-Laplacian}

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.


P-Laplacian

codex/p-laplacian-equation

p-Laplacian ( $Δ_{p} u = div (∣ D u ∣^{p - 2} D u)$ )

 Ancestors (6)

 Incoming links (1)

 Synonyms (1)

 Discussion (0)

 Articles by others on the same topic (1)

p-Laplacian (Δp​u=div(∣Du∣p−2Du))