Continuous dependence on forcing
= Continuous dependence on forcing
Solutions depend continuously on their forcing when convergence of the forcing in a specified <norm> implies convergence of solutions in a specified solution <norm>, with <boundary conditions> fixed. A uniform estimate $\|u-v\|_X\leq C\|f-g\|_Y$ is a stronger quantitative form, namely <Lipschitz continuity> of the solution map. The <monotonicity energy estimate for a semilinear Dirichlet problem> is an example.