Lagrange multipliers for evolution problems with constraints on the derivatives

• Autor(a) principal: Azevedo, Assis
• Data de Publicação: 2021
• Outros Autores: Rodrigues, José Francisco, Santos, Lisa
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/1822/72877
• topic: variational inequalities; sandpile problem; superconductivity problem; flow of thick fluids; problems with the biharmonic operator; first order vector fields of sunelliptic type; superconductivity problems; flows of thick fluids; first order vector fields of subelliptic type; Ciências Naturais::Matemáticas; Science & Technology

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.