Charles Darwin In Cambridge: The Most Joyful Years The Most Joyful Years

Charles Darwin's years as a student at the University of Cambridge were some of the most important and formative of his life. Thereafter he always felt a particular affection for Cambridge. For a time he even considered a Cambridge professorship as a career and sent three of his sons there to be educated. Unfortunately the remaining traces of what Darwin actually did and experienced in Cambridge have long remained undiscovered. Consequently his day- to-day life there has remained unknown and misunderstood. This book is based on new research, including newly discovered manuscripts and Darwin publications, and gathers together recollections of those who knew Darwin as a student. This book therefore reveals Darwin's time in Cambridge in unprecedented detail. (Publisher)

The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.

The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.

At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.

Contents:

• Preliminaries:
  • The Geometry of Banach Spaces
  • Spaces with Variable Exponent
• Sobolev Spaces with Variable Exponent:
  • Definition and Functional-analytic Properties
  • Sobolev Embeddings
  • Compact Embeddings
  • Riesz Potentials
  • Poincaré-type Inequalities
  • Embeddings
  • Hölder Spaces with Variable Exponents
  • Compact Embeddings Revisited
• The p(·)-Laplacian:
  • Preliminaries
  • The p (·)-Laplacian
  • Stability with Respect to Integrability
• Eigenvalues:
  • The Derivative of the Modular
  • Compactness and Eigenvalues
  • Modular Eigenvalues
  • Stability with Respect to the Exponent
  • Convergence Properties of the Eigenfunctions
• Approximation on Lp Spaces:
  • s -numbers and n -widths
  • A Sobolev Embedding
  • Integral Operators

Readership: Graduates and researchers interested in differential operators and function spaces.

Early life, 1809-1825 Edinburgh University, 1825-1827 Coming up to Cambridge First year at Cambridge Second year at Cambridge Third year at Cambridge Last terms at Cambridge Voyage of the Beagle - and return to Cambridge The origin of species and honorary Cambridge degree 1909 : the First Darwin Centenary in Cambridge 2009 : the Second Darwin Centenary in Cambridge.