A Compactness Result for Vector Elds with Divergence and Curl in L Q (() Involving Mixed Boundary Conditions
نویسنده
چکیده
It is shown that the space of all vector elds with divergence and curl in L q ((), q 2 such that the normal-component vanishes one part of @ and the tangential-component vanishes on the other, is compactly imbedded in L 2 (().
منابع مشابه
On the div-curl lemma in a Galerkin setting
Given a sequence of Galerkin spaces Xh of curl conforming vector fields, we state necessary and sufficient conditions under which it is true that the scalar product uh ·uh of two sequences of vector fields uh, uh ∈ Xh converging weakly in L, converges in the sense of distributions to the right limit, whenever uh is discrete divergence free and curluh is precompact in H−1. The conditions on Xh a...
متن کاملInverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...
متن کاملInverse Sturm-Liouville problem with discontinuity conditions
This paper deals with the boundary value problem involving the differential equation begin{equation*} ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity conditions at a point $ain (0,pi)$ begin{equation*} y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x), a_1 , a_2$ are rea...
متن کامل3-D Vector Tomography on Bounded Domains
This paper considers the problem of vector tomography on an arbitrary bounded domain in three dimensions. The probe transform of a vector eld is the inner product of the Radon transform of a vector eld with a unit vector, called the probe, which may be a function of the projection orientation. Previous work has given reconstruction formulas for arbitrary elds and for those known to be divergenc...
متن کاملA Remark on the Regularity of Solutions of Maxwell's Equations on Lipschitz Domains
Let ~ u be a vector eld on a bounded Lipschitz domain in R 3 , and let ~ u together with its divergence and curl be square integrable. If either the normal or the tangential component of ~ u is square inte-grable over the boundary, then ~ u belongs to the Sobolev space H 1=2 on the domain. This result gives a simple explanation for known results on the compact embedding of the space of solution...
متن کامل