Dear all, why the linearizaiton of the following PDE

$\displaystyle (1+u_y^2)u_{xx}-2u_xu_yu_{xy}+(1+u_x^2)u_{yy}=0$

is

$\displaystyle u_{xx}+u_{yy}=0?$

Thank you very much.

Indeed, I do not know what linearization means. Thank you in advance.

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- Oct 13th 2011, 07:11 AMxinglongdadaLinearization of a PDE
Dear all, why the linearizaiton of the following PDE

$\displaystyle (1+u_y^2)u_{xx}-2u_xu_yu_{xy}+(1+u_x^2)u_{yy}=0$

is

$\displaystyle u_{xx}+u_{yy}=0?$

Thank you very much.

Indeed, I do not know what linearization means. Thank you in advance.