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Conformally bending three-manifolds with boundary

Matthew Gursky, Jeffrey Streets, Micah Warren (2010)

Annales de l’institut Fourier

Given a three-dimensional manifold with boundary, the Cartan-Hadamard theorem implies that there are obstructions to filling the interior of the manifold with a complete metric of negative curvature. In this paper, we show that any three-dimensional manifold with boundary can be filled conformally with a complete metric satisfying a pinching condition: given any small constant, the ratio of the largest sectional curvature to (the absolute value of) the scalar curvature is less than this constant....

Conical diffraction by multilayer gratings: A recursive integral equation approach

Gunther Schmidt (2013)

Applications of Mathematics

The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in ℝ 2 coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with...

Conjetura de Kato sobre los abiertos de R.

Pascal Auscher, Philippe Tchamitchian (1992)

Revista Matemática Iberoamericana

We prove Kato's conjecture for second order elliptic differential operators on an open set in dimension 1 with arbitrary boundary conditions. The general case reduces to studying the operator T = - d/dx a(x) d/dx on an interval, when a(x) is a bounded and accretive function. We show for the latter situation that the domain of T is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function a(x).

Construction of compact constant mean curvature hypersurfaces with topology

Mohamed Jleli (2012)

Annales de l’institut Fourier

In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.

Contact problem of two elastic bodies. I

Vladimír Janovský, Petr Procházka (1980)

Aplikace matematiky

The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.

Contact problem of two elastic bodies. II

Vladimír Janovský, Petr Procházka (1980)

Aplikace matematiky

The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.

Contact problem of two elastic bodies. III

Vladimír Janovský, Petr Procházka (1980)

Aplikace matematiky

The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.

Continuity of solutions of a nonlinear elliptic equation

Pierre Bousquet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a nonlinear elliptic equation of the form div [a(∇u)] + F[u] = 0 on a domain Ω, subject to a Dirichlet boundary condition tru = φ. We do not assume that the higher order term a satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and φ satisfies a one-sided bounded slope condition, or when ais radial: a ( ξ ) = l ( | ξ | ) | ξ | ξ a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasingl:ℝ+ → ℝ+.

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