The Ornstein-Uhlenbeck semigroup in exterior domains

Wood, Ian; Geissert, M.; Heck, H.; Hieber, M., (2005) 'The Ornstein-Uhlenbeck semigroup in exterior domains', Archiv der Mathematik 86 pp.554-562 RAE2008

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

Hardy's inequality on exterior domains

Let Ω be a smooth exterior domain in ℝN and 1 < p < ∞. We prove that when p ≠ N, Hardy's LP inequality is valid on D01,p(Ω). ©2005 American Mathematical Society

Künstliche Randbedingungen und Algebraische Äquivalenzen in der Elastizitätstheorie

In dieser Arbeit werden zwei Aspekte bei Randwertproblemen der linearen Elastizitätstheorie untersucht: die Approximation von Lösungen auf unbeschränkten Gebieten und die Änderung von Symmetrieklassen unter speziellen Transformationen. Ausgangspunkt der Dissertation ist das von Specovius-Neugebauer und Nazarov in "Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type"(Math. Meth. Appl. Sci, 2004; 27) eingeführte Verfahren zur Untersuchung von Petrovsky-Systemen zweiter Ordnung in Außenraumgebieten und Gebieten mit konischen Ausgängen mit Hilfe der Methode der künstlichen Randbedingungen. Dabei werden für die Ermittlung von Lösungen der Randwertprobleme die unbeschränkten Gebiete durch das Abschneiden mit einer Kugel beschränkt, und es wird eine künstliche Randbedingung konstruiert, um die Lösung des Problems möglichst gut zu approximieren. Das Verfahren wird dahingehend verändert, dass das abschneidende Gebiet ein Polyeder ist, da es für die Lösung des Approximationsproblems mit üblichen Finite-Element-Diskretisierungen von Vorteil sei, wenn das zu triangulierende Gebiet einen polygonalen Rand besitzt. Zu Beginn der Arbeit werden die wichtigsten funktionalanalytischen Begriffe und Ergebnisse der Theorie elliptischer Differentialoperatoren vorgestellt. Danach folgt der Hauptteil der Arbeit, der sich in drei Bereiche untergliedert. Als erstes wird für abschneidende Polyedergebiete eine formale Konstruktion der künstlichen Randbedingungen angegeben. Danach folgt der Nachweis der Existenz und Eindeutigkeit der Lösung des approximativen Randwertproblems auf dem abgeschnittenen Gebiet und im Anschluss wird eine Abschätzung für den resultierenden Abschneidefehler geliefert. An die theoretischen Ausführungen schließt sich die Betrachtung von Anwendungsbereiche an. Hier werden ebene Rissprobleme und Polarisationsmatrizen dreidimensionaler Außenraumprobleme der Elastizitätstheorie erläutert. Der letzte Abschnitt behandelt den zweiten Aspekt der Arbeit, den Bereich der Algebraischen Äquivalenzen. Hier geht es um die Transformation von Symmetrieklassen, um die Kenntnis der Fundamentallösung der Elastizitätsprobleme für transversalisotrope Medien auch für Medien zu nutzen, die nicht von transversalisotroper Struktur sind. Eine allgemeine Darstellung aller Klassen konnte hier nicht geliefert werden. Als Beispiel für das Vorgehen wird eine Klasse von orthotropen Medien im dreidimensionalen Fall angegeben, die sich auf den Fall der Transversalisotropie reduzieren lässt.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

On multiple solutions of the exterior neumann problem involving critical sobolev exponent

In this paper we consider the exterior Neumann problem involving a critical Sobolev exponent. We establish the existence of two solutions having a prescribed limit at infinity.

The contribution of different androgen receptor domains to receptor dimerization and signaling

The androgen receptor (AR) is a ligand-activated transcription factor of the nuclear receptor superfamily that plays a critical role in male physiology and pathology. Activated by binding of the native androgens testosterone and 5-dihydrotestosterone, the AR regulates transcription of genes involved in the development and maintenance of male phenotype and male reproductive function as well as other tissues such as bone and muscle. Deregulation of AR signaling can cause a diverse range of clinical conditions, including the X-linked androgen insensitivity syndrome, a form of motor neuron disease known as Kennedy’s disease, and male infertility. In addition, there is now compelling evidence that the AR is involved in all stages of prostate tumorigenesis including initiation, progression, and treatment resistance. To better understand the role of AR signaling in the pathogenesis of these conditions, it is important to have a comprehensive understanding of the key determinants of AR structure and function. Binding of androgens to the AR induces receptor dimerization, facilitating DNA binding and the recruitment of cofactors and transcriptional machinery to regulate expression of target genes. Various models of dimerization have been described for the AR, the most well characterized interaction being DNA-binding domain- mediated dimerization, which is essential for the AR to bind DNA and regulate transcription. Additional AR interactions with potential to contribute to receptor dimerization include the intermolecular interaction between the AR amino terminal domain and ligand-binding domain known as the N-terminal/C-terminal interaction, and ligand-binding domain dimerization. In this review, we discuss each form of dimerization utilized by the AR to achieve transcriptional competence and highlight that dimerization through multiple domains is necessary for optimal AR signaling.

Domains of rural social work practice

Even though there is substantial agreement about the nature of rural contexts, practice principles, and factors influencing practice we still do not have a framework for organising this knowledge in a way that can directly inform the practitioner in their day-to-day work. In this paper, we introduce the concepts 'practice domains', 'domain location', and 'domain alignment' that, taken together, provide such a framework. We suggest that each practitioner works within a number of practice domains. A domain is a discourse about practice comprising narratives about how a social worker should practise and which factors they should take most account of in their practice decision making. Each practitioner, and each practice process, can be located somewhere within each domain (domain location) and also situated amongst domains according to their relative alignment with each of them (domain alignment). In this paper, we present this framework and show how it is useful for practitioners in understanding practice, identifying factors influencing it, and making practice decisions in immediate, concrete situations.

A general procedure for the derivation of principal domains of higher-order spectra

A general procedure to determine the principal domain (i.e., nonredundant region of computation) of any higher-order spectrum is presented, using the bispectrum as an example. The procedure is then applied to derive the principal domain of the trispectrum of a real-valued, stationary time series. These results are easily extended to compute the principal domains of other higher-order spectra

The influence of deprivation domains on malnutrition risk in outpatients with chronic obstructive pulmonary disease

Deprivation assessed using the Index of Multiple Deprivation (IMD) has been shown to be an independent risk factor for both malnutrition and mortality in outpatients with chronic obstructive pulmonary disease (COPD) (Collins et al., 2010a, b). IMD consists of a range of different deprivation domains, although it is unclear which ones are most closely linked to malnutrition. The aim of the current study was to investigate whether the relationship between malnutrition and deprivation was a general one, affecting all domains in a consistent manner, or specific, affecting only certain domains.