A functional-analytic framework for the study of elliptic equations on variable domains
José Manuel Vegas · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1990
Synopsis Given a decreasing sequence of domains Ωnconverging in measure to some domain Ω0, a sequence of subspacesVof a Hilbert spaceVis constructed in such a way that the convergence of the solutions ofu−Δu=fon Ωnwith Neumann Boundary Condition is given in terms of the convergence of the orthogonal projectionsPnonVn. Under dissipative assumptions, we can obtain continuation results for equations likeu−Δu=f(x,u∇u).