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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.
Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik. (matematik)
2016 (engelsk)Inngår i: Minimax Theory and its Applications, ISSN 2199-1413, Vol. 1, nr 2, s. 197-244Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2016. Vol. 1, nr 2, s. 197-244
Emneord [en]
second-order linear elliptic equations, mathematics
HSV kategori
Identifikatorer
URN: urn:nbn:se:hig:diva-18057ISI: 000408633700002Scopus ID: 2-s2.0-85033490912OAI: oai:DiVA.org:hig-18057DiVA, id: diva2:765343
Tilgjengelig fra: 2014-11-22 Laget: 2014-11-22 Sist oppdatert: 2018-03-13bibliografisk kontrollert

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