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Elliptic and Parabolic Problems
Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.
Function Spaces and Applications
Developed from the proceedings an international conference held in 1997, Function Spaces and Applications presents the work of leading mathematicians in the vital and rapidly growing field of functional analysis.
The Mitigation Doctrine
The “duty to mitigate loss” doctrine has been the object of study in many jurisdictions, which have interpreted and applied it in a wide range of situations and in different ways. In Brazil, however, only recent discussions have brought light to this subject. Worldwide, researchers have debated its nature – whether a duty or a principle – and the most proper way to address it (e.g.: if duty to mitigate loss or damages; duty to rescue; avoidable consequences doctrine). Studies have also detailed its application in different situations, such as in contracts and torts, among suppliers, consumers and national and international commerce, for instance. Ultimately, responding to the shift f...
Function Spaces in Analysis
This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.
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.
Mathematical Reviews
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