Partial Expansion of a Lipschitz Domain and Some Applications
نویسندگان
چکیده
We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.
منابع مشابه
The new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملDhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations
In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...
متن کاملApplication of the tan(phi/2)-expansion method for solving some partial differential equations
In this paper, the improved -expansion method is proposed to solve the Kundu–Eckhaus equation and Gerdjikov–Ivanov model. The applied method are analytical methods to obtaining the exact solutions of nonlinear equations. Here, the aforementioned methods are used for constructing the soliton, periodic, rational, singular and solitary wave solutions for solving some equations. We obtained furthe...
متن کاملThree Dimensional Analysis of Laminated Cylindrical Panels with Piezoelectric Layers
A semi-analytical solution is presented for three dimensional elastic analysis of finitelylong, simply supported, orthotropic, laminated cylindrical panels with piezoelectric layers subjected to outer pressure and electrostatic excitation. Both the direct and inverse piezoelectric effects are investigated. The solution is obtained through reducing the highly coupled partial differential equatio...
متن کاملNovel Four-Channel All Optical Demultiplexer Based on Square PhCRR for Using WDM Applications
Ring resonators have always been referred to as a highly flexible structurefor designing optical devices. In this study, we have designed and simulation a fourchannel optical demultiplexer using square photonic crystal ring resonator. The squarelattice constant for this purpose structure is used. The purposed structure has an averagecrosstalk, transmission coefficient, q...
متن کامل