variational equality

Hi everybody.

I have a question...I would like to know something about the solutions
g of the following equation, which holds for all f in the sobolev
space W^{1,2}(U), with U an open set in R^n

\int f g + \int \nabla f \nabla g = 0

where the integrals are done on U, \nabla is the gradient (in the weak
sense).

thank you,
vito

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