Gradient estimates in Orlicz space for nonlinear elliptic equations

In this paper we generalize gradient estimates in Lp space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique.     

Shape reconstruction of an inverse boundary value problem of two‐dimensional Navier–Stokes equations

This paper is concerned with the problem of the shape reconstruction of two‐dimensional flows governed by the Navier–Stokes equations. Our objective is to derive a regularized Gauss–Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss–Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical zoom for advection diffusion problems with localized multiscales

We investigate the Schwarz'domain decomposition algorithm for numerical zooms. Error estimates are given for nonmatching meshes for elliptic and parabolic partial differential equations. The method is applied to the security assessment of the burial of nuclear waste which is a typical multiscale problem for porous media flow. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Design equations for the assessment and FRP-strengthening of reinforced rectangular concrete columns under combined biaxial bending and axial loads

A simple procedure is proposed for the assessment of reinforced rectangular concrete columns under combined biaxial bending and axial loads and for the design of a correct amount of FRP-strengthening for underdesigned concrete sections. Approximate closed-form equations are developed based on the load contour method originally proposed by Bresler for reinforced concrete sections. The 3D failure surface is approximated along its contours, at a constant axial load, by means of equations given as the sum of the acting/resisting moment ratio in the directions of principal axes of the sections, raised to a power depending on the axial load, the steel reinforcement ratio, and the section shape. The method is extended to FRP-strengthened sections. Moreover, to make it possible to apply the load contour method in a more practical way, simple closed-form equations are developed for rectangular reinforced concrete sections with a two-way steel reinforcement and FRP strengthenings on each side. A comparison between the approach proposed and the fiber method (which is considered exact) shows that the simplified equations correctly represent the section interaction diagram. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 443–462, May–June, 2008.     

Decomposition and removability properties of John domains

In this paper we characterize John domains in terms of John domain decomposition property. In addition, we also show that a domain D in ℔ ⁿ is a John domain if and only if D\P is a John domain, where P is a subset of D containing finitely many points of D. The best possibility and an application of the second result are also discussed.     

On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups

We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic groups can have. In two previous papers, D. Bochiş and the second author studied the problem for noncubic groups. This paper deals with “full” cubic groups, while “quarter” cubic groups are left for a subsequent paper. Here, “full” and “quarter” refers to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston. This paper’s main result is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also find stereohedra with 17 facets for one of these groups. Research partially supported by the Spanish Ministry of Education and Science, grant number MTM2005-08618-C02-02.     

A research into the numerical method of Dirichlet's problem of complex Monge-Ampère equation on Cartan-Hartogs domain of the third type

Monge-Ampère equation is a nonlinear equation with high degree, therefore its numerical solution is very important and very difficult. In present paper the numerical method of Dirichlet's problem of Monge-Ampère equation on Cartan-Hartogs domain of the third type is discussed by using the analytic method. Firstly, the Monge-Ampère equation is reduced to the nonlinear ordinary differential equation, then the numerical method of the Dirichlet problem of Monge-Ampère equation becomes the numerical method of two point boundary value problem of the nonlinear ordinary differential equation. Secondly, the solution of the Dirichlet problem is given in explicit formula under the special case, which can be used to check the numerical solution of the Dirichlet problem.     

A sufficient condition for the existence of limit values of solutions of an elliptic equation on the boundary

We find a sufficient condition for the existence of a limit value of an elliptic equation solution on the domain boundary. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 436–449, December, 2008.     

Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement

Interactive vortex shedding in the multiply connected domain formed by a pair of circular cylinders is analysed by the FEM–FDM blending technique. The vorticity–streamfunction formulation is used to solve the incompressible Navier–Stokes equations at Re = 100, with the time-dependent wall streamfunctions determined from the pressure constraint condition and the far-field streamfunctions from the integral series formula developed earlier by the authors. The standard Galerkin finite element method is used in the relatively small FEM subdomain and the finite difference method based on the general co-ordinate system in the rest of the flow domain. Symmetric, antisymmetric and asymmetric wake patterns are obtained confirming the earlier experimental findings. The bistable nature of the asymmetric vortex shedding as well as the intermittent drifting from one status to the other between symmetric and antisymmetric wake patterns are reported.