weak solution to the inhomogeneous boundary value problem. Continuous dependence on the data It remains to investigate the dependence of on and . Let denote constants independent of and . By continuous dependence of on the right-hand side of its integral equation, there holds and thus, using that and by continuity of the trace extension operator, it follows that and the solution map is therefore continuous. See also Trace class Nuclear operators between Banach spaces References Leoni, Giovanni (2017). A First Course in Sobolev Spaces: Second Edition. Graduate Studies in Mathematics. 181. American Mathematical Society. pp. 734. Sobolev spaces Operator theory de:Sobolev-Raum#Spuroperator