Dirichlet-to-Neumann maps on bounded Lipschitz domains

The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The main objective of this paper is to present a systematic study of the Dirichlet-to-Neumann map and its inverse, the Neumann-to-Dirichlet map, in the framework of linear relations in Hilbert spaces. Our treatment is inspired by abstract methods from extension theory of symmetric operators, utilizes the general theory of linear relations and makes use of some deep results on the regularity of the solutions of boundary value problems on bounded Lipschitz domains

Consistent operator semigroups and their interpolation

Under a mild regularity condition we prove that the generator of the interpolation of two C0-semigroups is the interpolation of the two generators

H\"older estimates for parabolic operators on domains with rough boundary

We investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness and ellipticity on the coefficient function and very mild conditions on the geometry of the domain, including a very weak compatibility condition between the Dirichlet boundary part and its complement, we prove H\"older continuity of the solution in space and time.Comment: 1 figur

Godsdiens, evangelie en religie in die poësie met besondere verwysing na gedigte van Ida Gerhardt

It is characteristic of this famous poetess that she abhors evangelical poetry. She considers this kind of poetry often to be of poor quality, especially in the light of its explicit purpose to evangelize and convert readers to Christianity, h could be argued that the Dutch poetess Nel Benschop, of whom tens of thousands volumes of poetry are sold, writes such poetry. Despite her abhorrence of evangelical poetry, Gerhardt cannot summarily be regarded as an atheist artist. On the contrary, she may even be called a Christian poetess, but not in the dogmatic sense of the word. The impact of her work transcends the boundaries of Christianity. She often uses Christianity as a frame of reference along with Greek and Latin Classical references to give her poetry universality. To illustrate this I would like to compare her Easter poem ("Pasen") with some Easter poems of minor poets like Nel Benschop and l.L de Villiers. An analysis of the Easter poems shows that Gerhardt’s Easter poem obviously has a Christian framework but its implications are far wider

Communicating Mental Illness in the Black American Community

Human-human interactions are of central relevance for the success in professional and occupational environments, which also substantially influence quality of life. This is especially true in the case of individuals with high-functioning autism (HFA), who experience deficits in social cognition that often lead to social exclusion and unemployment. Despite good education and high motivation, individuals with HFA do not reach employment rates that are substantially higher than 50 %. This is an alarmingly high rate of unemployment considering that the United Nations have recently emphasized the inclusion of handicapped persons as a mandatory human right. To date, the specific needs of autistic persons with respect to their working environment are largely unexplored. It remains moreover an open question how support systems and activities, including newly developed communication devices for professional environments of individuals with HFA, should look like. The German health and social care systems are not adequately prepared for the proper support of this population. This leads us to suggest that supported employment programs should be developed for adults with HFA that specifically address their needs and requirements. Such programs should comprise (1) the adequate assessment of HFA, including a neuropsychological profile and an individual matching of persons' preferences with requirements of the working place, (2) on-the-job coaching activities that include systematic communication and interaction training, and (3) instruction of non-autistic peers, including colleagues and supervisors, about weaknesses and strengths of HFA

Integrability of irrotational silent cosmological models

We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearised silent models, but not in the general exact non-linear case. Thus there is a linearisation instability, and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class. Quantum Grav.; 16 pages Ioplpp

New explicit spike solution -- non-local component of the generalized Mixmaster attractor

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate non-colour printin

Quasi-Newtonian dust cosmologies

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function $N$ (the relativistic acceleration scalar potential) which evolves along the reference congruence according to $\dot{N} = \alpha \Theta N$ ($\alpha = {const}$), we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearising the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.Comment: 25 pages, LaTeX 2.09 (10pt), to appear in Classical and Quantum Gravity, Vol. 15 (1998