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Mixed variational approach to finding guaranteed estimates from solutions and right-hand sides of the second-order linear elliptic equations under incomplete data
T. Shevchenko Kyiv National University, Kyiv, Ukraine.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. (matematik)
2016 (English)In: Minimax Theory and its Applications, ISSN ISSN 2199-1413; EISSN 2199-1421, Vol. 1, no 2, 197-244 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the problem of guaranteed estimation of values of linear continuous functionals defined on solutions to mixed variational equations generated by linear elliptic problems from indirect noisy observations of these solutions. We assume that right-hand sides of the equations, as well as the second moments of noises in observations are not known; the only available information is that they belong to given bounded sets in the appropriate functional spaces. We are looking for linear with respect to observations optimal estimates of solutions of aforementioned equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms ofsolutions to special mixed variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. We study also the problem of guaranteed estimation of right-hand sides of mixed variational equations.

Place, publisher, year, edition, pages
2016. Vol. 1, no 2, 197-244 p.
Keyword [en]
second-order linear elliptic equations, mathematics
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:hig:diva-18057OAI: oai:DiVA.org:hig-18057DiVA: diva2:765343
Available from: 2014-11-22 Created: 2014-11-22 Last updated: 2016-11-28Bibliographically approved

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