There are two different functions f and g in an equation. I would like to make this equation into a weak formulation.
$$ \nabla^2f+\nabla^2 \ln g + a=0 $$
For example, if this equation is defined in x dimension, how can I make this to weak form? I'm not sure if there are two different test functions needed for each function. Please feel free to set a convenient boundary condition for solving