Constructive Aspects of the Dirichlet Problem
Дата
Авторы
Bridges,Douglas
Yuchuan,Wang
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
We examine, within the framework of Bishop's constructive mathematics, various classical methods for proving the existence of weak solutions of the Dirichlet Problem, with a view to showing why those methods do not immediately translate into viable constructive ones. In particular, we discuss the equivalence of the existence of weak solutions of the Dirichlet Problem and the existence of minimizers for certain associated integral functionals. Our analysis pinpoints exactly what is needed to find weak solutions of the Dirichlet Problem: namely, the computation of either the norm of a linear functional on a certain Hilbert space or, equivalently, the infimum of an associated integral functional. 1.) Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science, special issue editors D.S. Bridges, C.S. Calude, M.J. Dinneen and B. Khoussainov.
Ключевые слова
Dirichlet problem , Hilbert space , Bishop's constructive mathematics