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Uniform estimates for the parabolic Ginzburg-Landau equation
| Content Provider | CiteSeerX |
|---|---|
| Author | Bethuel, F. Orl, G. |
| Abstract | Abstract. We consider complex-valued solutions u " of the Ginzburg{Landau equation on a smooth bounded simply connected domain Ω of RN, N 2, where "> 0 is a small parameter. We assume that the Ginzburg{Landau energy E"(u") veries the bound (natural in the context) E"(u") M0j log "j, where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of u", as " ! 0, is to establish uniform Lp bounds for the gradient, for some p> 1. We review some recent techniques developed in the elliptic case in [7], discuss some variants, and extend the methods to the associated parabolic equation. |
| File Format | |
| Journal | ESAIM, C.O.C.V |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Parabolic Ginzburg-landau Equation Uniform Estimate Ginzburg Landau Equation Several Assumption Elliptic Case Uniform Lp Bound Complex-valued Solution Parabolic Equation M0j Log Connected Domain Asymptotic Analysis Recent Technique Important Step Boundary Data Ginzburg Landau Energy Small Parameter |
| Content Type | Text |
| Resource Type | Article |
