Variational inequalities with the duality operator in Banach spaces

Year 2020, Volume: 3 Issue: 2, 78 - 84, 30.06.2020

In-sook Kim

Abstract

We study variational inequality by way of metric projection in Banach spaces. The main method is to use a topological degree theory
for the class of operators of monotone type in Banach spaces. More precisely, some variational inequality associated with the duality operator
is considered. As applications, the problem is discussed in the Lebesgue spaces $L^p$ and the Sobolev spaces $W^{1,2}$.

Keywords

variational inequality, operators of monotone type, degree theory

References

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