Variational problems with non-constant gradient constraints

• Autor(es): Santos, Lisa
• Data: 2002
• Identificador Persistente: http://hdl.handle.net/1822/1555
• Origem: RepositóriUM - Universidade do Minho
• Assunto(s): Parabolic variational inequality; Parabolic PDE; Free boundary problem
• Tipo de Documento: Artigo
• Idioma: Inglês

Descrição

This paper studies existence, uniqueness, continuous dependence on the given data and the asymptotic behavior of the solution of an evolutive variational inequality with non-constant gradient constraint and homogeneous Dirichlet boundary condition. With assumptions on the given data, we prove existence of solution for a variational inequality with two obstacles, a Lagrange multiplier problem and an equation with gradient constraint. Equivalence of these problems with the variational inequality with gradient constraint is proved. An example of non-equivalence among these problems is given in order to show the necessity of the assumptions.