Work

Lagrange multipliers and characteristic functions

Year: 2025

Type: article

Abstract: We consider a stationary variational inequality with gradient constraint and obstacle. We prove that this problem can be described by an equation using a Lagrange multiplier and a characteristic function. The Lagrange multiplier contains information about the contact set of the modulus of the gradient of the solution with the gradient constraint, and the characteristic function is defined in the contact set of the solution with the obstacle. Moreover, given a convergent sequence of data, we prove the stability of certain corresponding solutions.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113382

Authors: Davide Azevedo, Lisa Santos

Institutions: Centro de Matemática, University of Minho

Language: English

Topic: Contact Mechanics and Variational Inequalities

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Fundação para a Ciência e a Tecnologia, Centro de Matemática, Universidade do Minho