One-dimensional variational problems are often neglected in favor of problems which use multiple integrals and partial differential equations, which are typically more difficult to handle. However, these problems and their associated ordinary differential equations do exhibit many of the same challenges and complexity of higher-dimensional problems, while being accessible to more students. This book for graduate students provides the first modern introduction to this subject. It emphasizes direct methods and provides an exceptionally clear view of the underlying theory. Except for standard...

The new series, International Mathematical Series is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday.

O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences.

Many generations of mathematicians have...

The main topics reflect the fields of mathematics in which Professor O.A. Ladyzhenskaya obtained her most influential results.

One of the main topics considered in the volume is the Navier-Stokes equations. This subject is investigated in many different directions. In particular, the existence and uniqueness results are obtained for the Navier-Stokes equations in spaces of low regularity. A sufficient condition for the regularity of solutions to the evolution Navier-Stokes equations in the three-dimensional case is derived and the stabilization of a solution to the Navier-Stokes...

Der zweite Band dieses Lehrbuchs der Analysis umfat den Stoff des zweiten Semesters eines mathematischen Grundstudiums fur Studierende der Mathematik, Physik und Informatik. Der klare und ubersichtliche Aufbau berucksichtigt, da schon fruhzeitig die mathematischen Hilfsmittel erortert werden, die zum Verstandnis der physikalischen Grundvorlesungen unerlalich sind. In Verbindung mit Band 1 ist so ein Leitfaden fur das Studium der Analysis entstanden, der das in den ersten beiden Studiensemestern zu erwerbende mathematische Grundwissen umfat. Ausfuhrliche Beweise und Erlauterungen sowie...

This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as weIl as Hamilton Jacobi theory and the classical theory of partial differential equations of first order. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus...

Osserman erzahlt lebendig und anschaulich eine Geschichte der Geometrie, von der Bestimmung der Erdgestalt und -grosse durch die alten Griechen uber das Problem der Kartierung der Weltkugel bis hin zur gekrummten Raumzeit, den Fraktalen und Buckyballs. Viele wird uberraschen, dass in der Mathematik nicht nur analytisches Denken zahlt, sondern dass Imagination, Phantasie und Kreativitat viel wichtiger sind. Dies und die Schonheit der Mathematik schlagen die Brucke zur Bildenden Kunst und Literatur, so nimmt Dante in seiner Gottlichen Komodie das Riemannsche Universum vorweg - zudem besteht...

Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for...

Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as...

Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular...