The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new.  Meer

This work is based on the lecture notes of the course M742: Topics in Partial Dif­ ferential Equations, which I taught in the Spring semester of 1997 at Indiana Univer­ sity.  Meer

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases.  Meer

Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.  Meer

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal...  Meer

This self-contained monograph presents extensions of the Moser–Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen–Cahn PDE model of phase transitions.  Meer

Harmonic maps are solutions to a natural geometrical variational prob­ lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions.  Meer

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal...  Meer

Nonlinear partial differential equations has become one of the main tools of mod­ ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes.  Meer

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences.  Meer

The study of spatial patterns in extended systems, and their evolution with time, poses challenging questions for physicists and mathematicians alike.  Meer

Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics.  Meer

* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs.  Meer

Covers phase space analysis methods, including microlocal analysis, and their applications to physics Treats the linear and nonnlinear aspects of...  Meer

The Italian school of Mathematical Analysis has long and glo­ rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati­ cal Analysis at the Scuola Normale Superiore di Pisa.  Meer

This collection of articles serves to commemorate the legacy of Joseph D'Atri, who passed away on April 29, 1993, a few days after his 55th birthday. Joe D' Atri is credited with several fundamental discoveries in ge­ ometry.  Meer

On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar".  Meer

Many boundary value problems are equivalent to Au=O (1) where A : X ---+ Y is a mapping between two Banach spaces.  Meer

The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H.  Meer