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A functional-analytic framework for the study of elliptic equations on variable domains

Published online by Cambridge University Press:  14 November 2011

José M. Vegas
José M. Vegas
Affiliation:
Departmento de Mateḿtica Aplicada, Facultad de Mateḿticas, Universidad Complutense, 28040-Madrid, Spain
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Synopsis

Given a decreasing sequence of domains Ωn converging in measure to some domain Ω0, a sequence of subspaces V of a Hilbert space V is constructed in such a way that the convergence of the solutions of u −Δu = f on Ωn with Neumann Boundary Condition is given in terms of the convergence of the orthogonal projections Pn on Vn. Under dissipative assumptions, we can obtain continuation results for equations like u −Δu = f(x,u ∇u).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 3-4 , 1990 , pp. 367 - 380
Copyright
Copyright © Royal Society of Edinburgh 1990

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