Critical phenomena in gravitational collapse
A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.
Critical point theory applied to a class of the systems of the superquadratic wave equations.
Critical point theory for nonsmooth energy functionals and applications.
Critical points for reaction-diffusion system with one and two unilateral conditions
We show the location of so called critical points, i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions.
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.
Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance
Critical points of embeddings of into Orlicz spaces
Critical points of solutions of elliptic equations in two variables
Critical points of solutions to the obstacle problem in the plane
Critical points of the Moser-Trudinger functional on a disk
On the unit disk we study the Moser-Trudinger functional and its restrictions , where for . We prove that if a sequence of positive critical points of (for some ) blows up as , then , and weakly in and strongly in . Using this fact we also prove that when is large enough, then has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.
Critical singular problems on unbounded domains.
Criticality conditions for a finite homogenized natural-uranium fueled reactor with prescribed thermal neutron flux
Crochet de Jacobi non local sur un revêtement et ses applications à l’étude de l’équation de Burgers
Croissance asymptotique des solutions de l'équation des ondes sur une variété riemannienne compacte à courbure négative
Cross-Diffusion Systems with Entropy Structure
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion systems with an additional Laplace structure. The boundedness-by-entropy method allows for global bounded weak solutions to certain diffusion systems. Furthermore, a partial result on the uniqueness of weak...
Crossover collision of scroll wave filaments.
Cubic Quasilinear wave equation and bilinear estimates
Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow
Curvature estimates for minimal hypersurfaces in singular spaces.