Аннотация:
We discuss some results on the convergence of minimizers and minimum values of integral and more general functionals on sets of functions defined by bilateral constraints in variable domains. We consider the case of regular constraints, i.e., constraints lying
in the corresponding Sobolev space, and the case where the lower constraint is zero and the upper constraint is an arbitrary nonnegative function.
The first case concerns a larger class of integrands and requires the positivity almost everywhere of the difference between the upper and lower constraints. In the second case, this requirement is absent. Moreover, in the latter case, the exhaustion condition of an nn-dimensional domain by a sequence of nn-dimensional domains plays an important role. We give a series of results involving this condition. In particular, using the exhaustion condition, we prove a certain convergence of sets of functions defined by bilateral (generally irregular) constraints in variable domains.
Ключевые слова:
Integral functional, Bilateral problem, Minimizer, Minimum value, ΓΓ-convergence of functionals, Strong connectedness of spaces, HH-convergence of sets, Exhaustion condition.
Образец цитирования:
Alexander A. Kovalevsky, “Convergence of solutions of bilateral problems in variable domains and related questions”, Ural Math. J., 3:2 (2017), 51–66
\RBibitem{Kov17}
\by Alexander~A.~Kovalevsky
\paper Convergence of solutions of bilateral problems in variable domains and related questions
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 2
\pages 51--66
\mathnet{http://mi.mathnet.ru/umj43}
\crossref{https://doi.org/10.15826/umj.2017.2.008}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3746952}
\elib{https://elibrary.ru/item.asp?id=32334099}
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https://www.mathnet.ru/rus/umj43
https://www.mathnet.ru/rus/umj/v3/i2/p51
Эта публикация цитируется в следующих 3 статьяx:
Alexander A. Kovalevsky, “Approximation in W1,pW1,p-norms of solutions of minimum problems with bilateral constraints in variable domains”, Boll Unione Mat Ital, 2025
Alexander A. Kovalevsky, “On the convergence of solutions of variational problems with pointwise functional constraints in variable domains”, J Math Sci, 254:3 (2021), 375
Alexander Kovalevsky, “On the convergence of solutions of variational problems with pointwise functional constraints in variable domains”, UMB, 17:4 (2020), 509
Цитирование в формате AMSBIB
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