RepositóriUM Collection: Artigos (Papers)
http://hdl.handle.net/1822/1231
Artigos (Papers)2019-11-16T23:09:48ZOn regular implicit operations
http://hdl.handle.net/1822/10493
<b>Title</b>: On regular implicit operations
<b>Author(s)</b>: Almeida, Jorge; Azevedo, Assis
<b>Type</b>: article2010-03-17T17:06:45ZThe nonlinear problem of two membranes
http://hdl.handle.net/1822/5891
<b>Title</b>: The nonlinear problem of two membranes
<b>Author(s)</b>: Santos, Lisa
<b>Abstract(s)</b>: The problem of finding the position of two membranes, one constrained by the other, attached to rigid supports, subjected to external forces, is considered. It is proved existence of solution, if we assume a compatibility condition relating the mean curvature of the boundary of the set where the problem is defined and the given data. It is also proved the W^{2,p} regularity of the solution for P greater or equal to 1.
<b>Type</b>: article2006-12-12T09:48:37ZThe N-membranes problem for quasilinear degenerate systems
http://hdl.handle.net/1822/2901
<b>Title</b>: The N-membranes problem for quasilinear degenerate systems
<b>Author(s)</b>: Azevedo, Assis; Rodrigues, José Francisco; Santos, Lisa
<b>Abstract(s)</b>: We study the regularity of the solution of the variational inequality for the problem of N-membranes in equilibrium with a degenerate operator of p-Laplacian type, 1 < p < ∞, for which
we obtain the corresponding Lewy-Stampacchia inequalities. By considering the problem as a system coupled through the characteristic functions of the sets where at least two membranes are in contact, we analyze
the stability of the coincidence sets.
<b>Type</b>: article2005-09-14T10:10:02ZConvergence of convex sets with gradient constraint
http://hdl.handle.net/1822/2899
<b>Title</b>: Convergence of convex sets with gradient constraint
<b>Author(s)</b>: Azevedo, Assis; Santos, Lisa
<b>Abstract(s)</b>: Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega)
(p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented.
We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.
<b>Type</b>: article2005-09-14T09:30:18ZA parabolic quasi-variational inequality arising in a superconductivity model
http://hdl.handle.net/1822/2898
<b>Title</b>: A parabolic quasi-variational inequality arising in a superconductivity model
<b>Author(s)</b>: Rodrigues, José Francisco; Santos, Lisa
<b>Abstract(s)</b>: We consider the existence of solutions for a parabolic quasilinear problem with a gradient constraint which threshold depends on the solution itself. The problem may be considered as a quasi-variational inequality and the existence of solution is shown by considering a suitable family of approximating quasilinear equations of p-Laplacian type. A priori estimates on the time derivative of the approximating solutions and on the nonlinear diffusion coefficients are used in the passage to the limit, as well as a suitable sequence of convex sets with variable gradient constraint. The asymptotic behaviour as t → ∞
is also considered, and the solutions of the quasi-variational inequality are shown to converge, at least for subsequences, to a solution of a stationary quasi-variational inequality. These results can be applied to the critical-state model of type-II superconductors in longitudinal geometry.
<b>Description</b>: 35K85 (primary), 35K55, 35R35 (secondary)
<b>Type</b>: article2005-09-14T08:51:59Z