Abstract. In this article we deal with a sequence of functionals defined on weighted Sobolev spaces. The spaces are associated with a sequence of domains Ω s contained in a bounded domain Ω of R n . The main structural components of the functionals are integral functionals whose integrands satisfy a growth and coercivity condition with a weight and additional terms ψ s ∈ L 1 (Ω s ) . For the given functionals we consider variational problems with sets of constraints for functions v of the kind h (x,v(x)) 0 a. e. in Ω s , where h : Ω × R → R . We establish conditions on h and ψ s and on the given domains, weighted spaces and functionals under which solutions of the variational problems under consideration converge in a certain sense to a solution of a limit variational problem with the set of constraints defined by the same function h . (2000): 49J45, 49J40, 35B27.
Mathematics subject classification
We consider weighted Sobolev spaces correlated with a sequence of n-dimensional domains. We prove a theorem on the choice of a subsequence Γ-convergent to an integral functional defined on a "limit" weighted Sobolev space from a sequence of integral functionals defined on the spaces indicated.
The paper presents the data obtained in the study of the health of the ecosystems in a number of recreational areas of the Black Sea and the Eastern Gulf of Finland. Prompt assessment of the health of the ecosystems was carried out by testing the health of adult bivalve mollusks inhabiting them, using the functional load method based on the analysis of their heart rate measured by a fiber-optic bioelectronic system. The goal of the study is to test the innovative bioindication technology developed earlier by the authors on the basis of the above-mentioned method in the regional programs for environmental monitoring of the ecosystems of coastal marine and freshwater recreational water areas (using the example of a number of water areas of Sevastopol, as well as several freshwater areas of the Kurortniy District of St. Petersburg. It has been established that the functional state of mollusks may serve as an indicator of excessive pollution of coastal waters by the objects that discharge insufficiently treated wastewater from their local treatment facilities, including household wastewater. The technology applied in this study for the assessment of functional state of local species of molluscs may be effectively used to solve the problems of early diagnostics of alterations in the health status of coastal aquatic ecosystems and contribute to ensuring the ecological safety of recreational water areas, serving as an infobase for the development of science-based environmental management decisions. Taking into account a high expressiveness and easy-to-use technology applied in the study (which does not require expertise for its practical implementation), this technology may be considered as the best available technology for biomonitoring the water quality of recreational waters in Russia.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.