Conformally Invariant Systems of Nonlinear PDE of Liouville Type.
Conical diffraction by multilayer gratings: A recursive integral equation approach
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 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.
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).
Connection between finite volume and mixed finite element methods
Constant Boundary value problem for a quasilinear elliptic system.
Constant Coefficient Differential Operators with Slowly Spreading Solutions.
Constant sign and nodal solutions for problems with the -Laplacian and a nonsmooth potential using variational techniques.
Construction de laplaciens dont une partie finie (avec multiplicités) du spectre est donnée
Construction of a Singular Elliptic-Harmonic Measure.
Construction of compact constant mean curvature hypersurfaces with topology
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.
Construction of Singular Solutions to the P-Harmonic Equation and its Limit Equation for P = ... .
Construction of the Leray-Schauder degree for elliptic operators in unbounded domains
Construction of the wave group for higher order elliptic boundary value problems
Contact problem of two elastic bodies. I
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
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
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, curvature, and the general covariance of optimal transportation
Continuity Estimates for Solutions to the Prescribed-Curvature Dirichlet Problem.
Continuity of solutions of a nonlinear elliptic equation
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 for some increasingl:ℝ+ → ℝ+.
Continuity of solutions of linear, degenerate elliptic equations
We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.