Page 1 Next

Displaying 1 – 20 of 64

Showing per page

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

Ayman Kachmar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.

Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture

Peter Knabner, Jean E. Roberts (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy−Forchheimerlaw while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy−Forchheimerlaw is the governing equation throughout the domain. We show existence and uniqueness of the solution...

Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian

Sundararaja Ramaswamy (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The aim of this paper is to characterize the u.s.c. (resp. l.s.c.) viscosity sub (resp. super) solutions of the Laplacian which do not take the value + (resp. - ) as precisely the sub (resp. super) harmonic functions.

Mean curvature properties for p -Laplace phase transitions

Berardino Sciunzi, Enrico Valdinoci (2005)

Journal of the European Mathematical Society

This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of p -Laplacian type and a double well potential h 0 with suitable growth conditions. We prove that level sets of solutions of Δ p u = h 0 ' ( u ) possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.

Metodi variazionali e topologici nello studio delle equazioni di Schrödinger nonlineari agli stati stazionari

Silvia Cingolani (2001)

Bollettino dell'Unione Matematica Italiana

In the present paper we survey some recents results concerning existence of semiclassical standing waves solutions for nonlinear Schrödinger equations. Furthermore, from Maxwell's equations we derive a nonlinear Schrödinger equation which represents a model of propagation of an electromagnetic field in optical waveguides.

Model problems from nonlinear elasticity: partial regularity results

Menita Carozza, Antonia Passarelli di Napoli (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we prove that every weak and strong local minimizer u W 1 , 2 ( Ω , 3 ) of the functional I ( u ) = Ω | D u | 2 + f ( Adj D u ) + g ( det D u ) , where u : Ω 3 3 , f grows like | Adj D u | p , g grows like | det D u | q and 1<q<p<2, is C 1 , α on an open subset Ω 0 of Ω such that 𝑚𝑒𝑎𝑠 ( Ω Ω 0 ) = 0 . Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate choice of the test functions. The limit case p = q 2 is also treated for weak local minimizers. ...

Monotone operators in divergence form with x -dependent multivalued graphs

Gilles Francfort, François Murat, Luc Tartar (2004)

Bollettino dell'Unione Matematica Italiana

We prove the existence of solutions to - div a x , grad u = f , together with appropriate boundary conditions, whenever a x , e is a maximal monotone graph in e , for every fixed x . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a 45 rotation, for every fixed x ; in other words, the graph d a x , e is defined through d - e = φ x , d + e , where φ is a Carathéodory contraction in R N . This definition is shown to be equivalent to the fact that a ( x , ) is pointwise monotone...

Currently displaying 1 – 20 of 64

Page 1 Next