3,337 research outputs found
Integral formulas for Levi curvature PDE’s and applications to isoperimetric inequalities and to symmetry problems
No full textPreface to the Special Issue: Nonlinear PDEs and geometric analysis – Dedicated to Neil Trudinger on the occasion of his 80th birthday
No full textThis contribution is the preface of the Special Issue: Nonlinear PDEs and geometric analysis – Dedicated to Neil Trudinger on the occasion of his 80th birthday
On the local theory of prescribed Jacobian equations
No full textWe develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory
Facing the Future: the Changing Shape of Academic Skills Support at Bournemouth University
No full textThis paper explores the potential impact of changes to higher education in England on student expectations, engagement, lifestyles and diversity, and outlines implications for the development of digital literacy within academic skills support at Bournemouth University (BU). We will investigate how tackling resource constraints with organisational change can also enable efficient, centralised provision of support materials that utilise networks to overcome the risk of fragmented support for digital literacy. We will also look at how changing delivery modes for support can accommodate changing student lifestyles whilst tackling a weakness of centralised support for digital literacy: that it can become detached from the student’s subject-focused academic practice. Finally we will explore how involving students in developing support can help us to face changes to student expectations and engagement whilst ensuring that materials are authentic and speak to learners in their own voice
Nonlinear oblique boundary value problems for nonlinear elliptic equations
No full textWe consider the nonlinear oblique derivative boundary value problem for quasilinear and fully nonlinear uniformly elliptic partial differential equations of second order. The elliptic operators satisfy natural structure conditions as introduced by Trudinger in the study of the Dirichlet problem while for the boundary operators we formulate general structure conditions which embrace previously considered special cases such as the capillarity condition. The resultant existence theorems include previous work such as that of Lieberman on quasilinear equations and Lions and Trudinger on Neumann boundary conditions.</p
Schauder estimates for fully nonlinear elliptic difference operators
No full textIn this paper, we are concerned with discrete Schauder estimates for solutions of fully nonlinear elliptic difference equations. Our estimates are discrete versions of second derivative Holder estimates of Evans, Krylov and Safonov for fully nonlinear elliptic partial differential equations. They extend previous results of Holt by for the special case of functions of pure second-order differences on cubic meshes. As with Holtby's work, the fundamental ingredients are the pointwise estimates of Kuo-Trudinger for linear difference schemes on general meshes
Why Privacy Matters: An Interview with Neil Richards
No full textProfessor Daniel J. Solove discusses the book \u27Why Privacy Matters\u27 and the future of privacy with the author, Professor Neil Richards
Interview with AntipodeFoundation.org: “Much More Than You Think: The Spatialities of Italian Autonomy” – Interview with Neil Gray, author of “Beyond the Right to the City: Territorial Autogestion and the Take over the City Movement in 1970s Italy”
No full textNo abstract available
Jere Nash Interview with Neil McMillen (Part 2 of 2)
No full textInterview conducted by author Jere Nash with University of Southern Mississippi history professor Neil R. McMillen in the process of writing Mississippi Politics: The Struggle for Power, 1976-2006. Topics discussed include Aaron Henry; race relations after the civil rights movement; and William Winter
On the classical solvability of near field reflector problems
No full textIn this paper we prove the existence of classical solutions to near field reflector problems, both for a point light source and for a parrallel light source, with planar recievers. These problems involve monge-Ampere type equations, subject to nonlinear oblique boundary conditions. Our approach builds on earlier work in the optimal transportation case by Trudinger and Wang and makes use of a recent extension of degree theory to oblique boundary conditioins by Li, Liu and Nguyen
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