Lawrence C. Evans

Luis A. Caffarelli

Luigi Ambrosio

Michael G. Crandall

Nicola Fusco

Centro internazionale matematico estivo. Summer School

E. Mascolo

With a historical overview by Elvira Mascolo

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 27 - July 2, 2005

Calculus of Variations and Nonlinear Partial Differential Equations

Panagiotis E. Souganidis

Martino Bardi

Halil M. Soner

The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, June, 12 - 20, 1995

Viscosity Solutions and Applications

Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm’s method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter’s product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 17–19, 1977

Nonlinear Evolution Equations

Michael G. Crandall

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