Abstract:
We prove the existence of generalized Lagrange multipliers for a class of evolution problems for linear differential operators of different types subject to constraints on the derivatives. Those Lagrange multipliers and the respective solutions are stable for the vanishing of the coercive parameter and are naturally associated with evolution variational inequalities with time-dependent convex sets of gradient type. We apply these results to the sandpile problem, to superconductivity problems, to flows of thick fluids, to problems with the biharmonic operator, and to first order vector fields of subelliptic type.
Keywords:
variational inequalities, sandpile problem, superconductivity problems, flows of thick fluids, problems with the biharmonic operator, first order vector fields of subelliptic type.
The research of A. Azevedo and L. Santos was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Fundação para a Ciência e a Tecnologia,” through the Project UID/MAT/00013/2013, and the one by J. F. Rodrigues was done partially in the framework of the Project PTDC/MAT-PUR/28686/2017.
Citation:
A. Azevedo, J.-F. Rodrigues, L. Santos, “Lagrange multipliers for evolution problems with constraints on the derivatives”, Algebra i Analiz, 32:3 (2020), 65–83; St. Petersburg Math. J., 32:3 (2021), 435–448
\Bibitem{AzeRodSan20}
\by A.~Azevedo, J.-F.~Rodrigues, L.~Santos
\paper Lagrange multipliers for evolution problems with constraints on the derivatives
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 3
\pages 65--83
\mathnet{http://mi.mathnet.ru/aa1700}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 3
\pages 435--448
\crossref{https://doi.org/10.1090/spmj/1655}
Linking options:
https://www.mathnet.ru/eng/aa1700
https://www.mathnet.ru/eng/aa/v32/i3/p65
This publication is cited in the following 1 articles:
José Francisco Rodrigues, Riccardo Scala, “Dynamics of a viscoelastic membrane with gradient constraint”, Journal of Differential Equations, 317 (2022), 603
Citation in format AMSBIB
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