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Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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Harnack inequality for the minimal surface equation

We consider the minimal surface equation $$ (1+|\nabla u|^2) \, \Delta u=\sum_{i,j=1}^n\partial_iu \, \partial_ju \, \partial_{ij}u\quad\hbox{in $B_1\subset\mathbb R^n.$} $$ If $u\in C^2(B_1)$ is a po …