Equations of curvature

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the compactness result of [35]. 1.

48p dontetvui 17-01-2013 59 7   Download

In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Amp`re equation when the inhomogee neous term is only assumed to be H¨lder continuous. As a consequence of our o approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation.

38p dontetvui 17-01-2013 48 8   Download

For the complex parabolic Ginzburg-Landau equation, we prove that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke’s weak formulation. The only assumption is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. Introduction In this paper we study the asymptotic analysis, as the parameter ε goes to zero, of the complex-valued parabolic Ginzburg-Landau equation for functions uε :

128p noel_noel 17-01-2013 42 7   Download

This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordstr¨m data, o the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose. ...

55p tuanloccuoi 04-01-2013 57 6   Download

Average depth model has a variety of applications in hydraulic engineering, especially in applications that flow depth is much smaller than the width of the flow. In this method the vertical variation is negligible and the hydraulic variables average integrated from channel bed to the surface free for the vertical axis. in equations arising management, pure hydrostatic pressure is assumed that not really valid in the case of flow in the bed is curved and can not be described curvature effects of the bed.

127p gauhaman123 17-11-2011 105 16   Download