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Regularity Theory (regularity + theory)
Selected AbstractsReconciling situational social psychology with virtue ethicsINTERNATIONAL JOURNAL OF MANAGEMENT REVIEWS, Issue 3 2008Surendra Arjoon For the past four decades, debate has occurred in respect of situational social psychology and virtue ethics. This paper attempts to reconcile this debate. Situationists propose a fragmentation theory of character (each person has a whole range of dispositions, each of which has a restricted situational application) and do not subscribe to a regularity theory of character (behaviour is regulated by long-term dispositions). In order to support this view, they cite a number of experiments. It is proposed that the substantive claims made by situationist social psychologists, for the most part, do not undermine or disagree with an Aristotelian virtue ethics perspective, but stem from a misunderstanding of concepts of moral character, faulty conclusions and generalizations in respect of experimental results. Situationists take a narrow view of character and morality. Evidence from organizational behaviour and managerial research literature supports the view that both situational (organizational) features and inner characteristics (including virtues) are powerful influences and determinants of morally upright and morally deviant behaviour. The role of practical judgement in bridging these views is discussed. As a way forward in reconciling situational social psychology with virtue ethics, the paper proposes an Aristotelian,Thomistic framework to overcome some of the problems associated with inadequate regulative ideals in building a normative moral theory. [source] Non-linear initial boundary value problems of hyperbolic,parabolic type.MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2002A general investigation of admissible couplings between systems of higher order. This is the second part of an article that is devoted to the theory of non-linear initial boundary value problems. We consider coupled systems where each system is of higher order and of hyperbolic or parabolic type. Our goal is to characterize systematically all admissible couplings between systems of higher order and different type. By an admissible coupling we mean a condition that guarantees the existence, uniqueness and regularity of solutions to the respective initial boundary value problem. In part 1, we develop the underlying theory of linear hyperbolic and parabolic initial boundary value problems. Testing the PDEs with suitable functions we obtain a priori estimates for the respective solutions. In particular, we make use of the regularity theory for linear elliptic boundary value problems that was previously developed by the author. In part 2 at hand, we prove the local in time existence, uniqueness and regularity of solutions to the quasilinear initial boundary value problem (3.4) using the so-called energy method. In the above sense the regularity assumptions (A6) and (A7) about the coefficients and right-hand sides define the admissible couplings. In part 3, we extend the results of part 2 to non-linear initial boundary value problems. In particular, the assumptions about the respective parameters correspond to the previous regularity assumptions and hence define the admissible couplings now. Moreover, we exploit the assumptions about the respective parameters for the case of two coupled systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Non-linear initial boundary value problems of hyperbolic,parabolic type.MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2002A general investigation of admissible couplings between systems of higher order. This is the third part of an article that is devoted to the theory of non-linear initial boundary value problems. We consider coupled systems where each system is of higher order and of hyperbolic or parabolic type. Our goal is to characterize systematically all admissible couplings between systems of higher order and different type. By an admissible coupling we mean a condition that guarantees the existence, uniqueness and regularity of solutions to the respective initial boundary value problem. In part 1, we develop the underlying theory of linear hyperbolic and parabolic initial boundary value problems. Testing the PDEs with suitable functions we obtain a priori estimates for the respective solutions. In particular, we make use of the regularity theory for linear elliptic boundary value problems that was previously developed by the author. In part 2, we prove the local in time existence, uniqueness and regularity of solutions to quasilinear initial boundary value problems using the so-called energy method. In the above sense the regularity assumptions about the coefficients and right-hand sides define the admissible couplings. In part 3 at hand, we extend the results of part 2 to the nonlinear initial boundary value problem (4.2). In particular, assumptions (B8) and (B9) about the respective parameters correspond to the previous regularity assumptions and hence define the admissible couplings now. Moreover, we exploit assumptions (B8) and (B9) for the case of two coupled systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Sharp regularity results on second derivatives of solutions to the Monge-Ampère equation with VMO type dataCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2009Qingbo Huang We establish interior estimates for Lp -norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge-Ampère equation det D2u = f(x) with zero boundary value, where f(x) is strictly positive, bounded, and satisfies a VMO-type condition. These estimates develop the regularity theory of the Monge-Ampère equation in VMO-type spaces. Our Orlicz estimates also sharpen Caffarelli's celebrated W2, p -estimates. © 2008 Wiley Periodicals, Inc. [source] | ||||||||||