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TitleVariational and quasivariational inequalities with first order constraints
Author(s)Azevedo, Assis
Miranda, Fernando
Santos, Lisa
KeywordsVariational inequality
Quasivariational inequality
Lagrange multiplier
Issue date2013
JournalJournal of Mathematical Analysis and Applications
Abstract(s)We study the existence of solutions of stationary variational and quasivariational inequalities with curl constraint, Neumann type boundary condition and a p-curl type operator. These problems are studied in bounded, not necessarily simply connected domains, with a special geometry, and the functional framework is the space of divergence-free functions with curl in $\boldsymbol L^p$ and null tangential or normal traces. The analogous variational or quasivariational inequalities with a gradient constraint are also studied, considering Neumann or Dirichlet non-homogeneous boundary conditions. The existence of a generalized solution for a Lagrange multiplier problem with homogeneous Dirichlet boundary condition and the equivalence with the variational inequality is proved in the linear case, for an arbitrary gradient constraint.
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AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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