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Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure
In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data. The first part of the monograph, which can be read...
Learning from 50 Years of Aboriginal Alcohol Programs
This open access book deals with community-based attempts on the part of Aboriginal communities and groups in Australia to address harms arising from alcohol misuse. Alcohol-related harms are viewed as both a product of colonisation and dispossession and a contributor to ongoing social, economic and health-related disadvantage, both in Australia and in other countries with colonised Indigenous populations, such as Canada, the US and New Zealand. This book contributes to an evidence-base by bringing together a selection of existing Australian documents considered by the editors to have continuing relevance to all those concerned with dealing with alcohol-related harms among Aboriginal peoples, These are contextualised in original chapters that recount key events, ideas, and programs. The book is a practical resource for all people and groups concerned with addressing Aboriginal and Torres Strait Islander alcohol-related harms, both at the community level and at the level of policy-making and administration.
Integro-Differential Elliptic Equations
Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutio...
Elliptic Boundary Value Problems with Fractional Regularity Data
A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.
Maximal Function Methods for Sobolev Spaces
This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Responding to the Oppression of Addiction, Fourth Edition
Responding to the Oppression of Addiction brings together the voices of over 40 academics and social work practitioners from across Canada to provide a diverse and multidimensional perspective to the study of addiction. This thoroughly updated edition features eight new chapters and streamlines the content of the previous editions, with chapters condensed and combined to create a more accessible text. The fourth edition features new content on themes such as residential schools, prevention initiatives, special needs of different populations, policy perspectives framed within an anti-oppression standpoint, cognitive behavioral therapy, and the emerging topic of problem gambling. Returning cha...
Cases on Current Issues, Challenges, and Opportunities in School Counseling
The counseling profession has greatly evolved from its vocational roots in the early 20th century. New professional demands resulting from dynamic student needs are once again reshaping the field of educational counseling. Contemporary issues facing students and schools often require a multi-disciplinary problem-solving approach. Cases on Current Issues, Challenges, and Opportunities in School Counseling showcases the interdisciplinary work done at the intersection of teaching and learning to support holistic student development in a PK-12 educational setting. The book presents current cases that illustrate common challenges and provide solutions or examples of approaches to guide educational practitioners in their development and work. Covering topics such as cultural proficiency, parental empowerment, and professional identity formulation, this casebook is an essential resource for educational counselors, school counselors-in-training, educators, administrators, pre-service teachers, teacher educators, researchers, and academicians.
