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Let [itex] u[/itex] defined in region [itex] \Omega[/itex] with boundary [itex] \Gamma[/itex].

If [itex] u = 0 \hbox { on the boundary } \Gamma[/itex], then [itex] u = 0 \hbox { in the region } \Omega[/itex].

The way to look at this, suppose [itex] u[/itex] is function of x component called Xand y component called Y. So either u=XY or u=X+Y.

1) If u=XY, u=0 mean either X or Y equal zero on [itex] \Gamma[/itex]. That can only happen if X or Y is identically equal to zero within the range of x or y.

2) If u=X+Y, u=0 means both X and Y identically equal to zero within the range of x and y.

Am I correct?

I am confuse, if I declare u=0 only on [itex] \Gamma[/itex] and equal to x+y anywhere else, then the assertion cannot not be true!!!! Please help.

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# Question about function defined in a region using Green's identities.

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