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The aim of this book is to present different aspects of the deep
interplay between Partial Differential Equations and Geometry. It
gives an overview of some of the themes of recent research in the
field and their mutual links, describing the main underlying ideas,
and providing up-to-date references.Collecting together the lecture
notes of the five mini-courses given at the CIME Summer School held
in Cetraro (Cosenza, Italy) in the week of June 19-23, 2017, the
volume presents a friendly introduction to a broad spectrum of
up-to-date and hot topics in the study of PDEs, describing the
state-of-the-art in the subject. It also gives further details on
the main ideas of the proofs, their technical difficulties, and
their possible extension to other contexts. Aiming to be a primary
source for researchers in the field, the book will attract
potential readers from several areas of mathematics.
The papers in this book originate from lectures which were held at
the "Vienna Workshop on Nonlinear Models and Analysis" - May 20-24,
2002. They represent a cross-section of the research field Applied
Nonlinear Analysis with emphasis on free boundaries, fully
nonlinear partial differential equations, variational methods,
quasilinear partial differential equations and nonlinear kinetic
models.
The papers in this book originate from lectures which were held at
the "Vienna Workshop on Nonlinear Models and Analysis" - May 20-24,
2002. They represent a cross-section of the research field Applied
Nonlinear Analysis with emphasis on free boundaries, fully
nonlinear partial differential equations, variational methods,
quasilinear partial differential equations and nonlinear kinetic
models.
The regularity theory of free boundaries flourished during the late
1970s and early 1980s and had a major impact in several areas of
mathematics, mathematical physics, and industrial mathematics, as
well as in applications. Since then the theory continued to evolve.
Numerous new ideas, techniques, and methods have been developed,
and challenging new problems in applications have arisen. The main
intention of the authors of this book is to give a coherent
introduction to the study of the regularity properties of free
boundaries for a particular type of problems, known as
obstacle-type problems. The emphasis is on the methods developed in
the past two decades. The topics include optimal regularity,
nondegeneracy, rescalings and blowups, classification of global
solutions, several types of monotonicity formulas, Lipschitz,
$C^1$, as well as higher regularity of the free boundary, structure
of the singular set, touch of the free and fixed boundaries, and
more. The book is based on lecture notes for the courses and
mini-courses given by the authors at various locations and should
be accessible to advanced graduate students and researchers in
analysis and partial differential equations.
With the increased taxonomic stability and uniformity brought about
by such authoritative synonymy, the entire flora of North America
can now be viewed as a whole for comparison with the floras of
other areas of the world. In all, more than 55,000 species of
vascular plants in 255 families, are fully treated. All entries are
arranged alphabetically by family, genus, species, subspecies, and
variety and fully indexed to the generic level.
A UNC Press Enduring Edition -- UNC Press Enduring Editions use the
latest in digital technology to make available again books from our
distinguished backlist that were previously out of print. These
editions are published unaltered from the original, and are
presented in affordable paperback formats, bringing readers both
historical and cultural value.
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