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Recent Developments in Nonlinear Partial Differential Equations
Edited by: Donatella Danielli, Purdue University, West Lafayette, IN
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Contemporary Mathematics
2007; 133 pp; softcover
Volume: 439
ISBN-10: 0-8218-3740-0
ISBN-13: 978-0-8218-3740-5
List Price: US$50
Member Price: US$40
Order Code: CONM/439
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This volume contains research and expository articles based on talks presented at the 2nd Symposium on Analysis and PDEs, held at Purdue University. The Symposium focused on topics related to the theory and applications of nonlinear partial differential equations that are at the forefront of current international research. Papers in this volume provide a comprehensive account of many of the recent developments in the field.

The topics featured in this volume include: kinetic formulations of nonlinear PDEs; recent unique continuation results and their applications; concentrations and constrained Hamilton-Jacobi equations; nonlinear Schrödinger equations; quasiminimal sets for Hausdorff measures; Schrödinger flows into Kähler manifolds; and parabolic obstacle problems with applications to finance.

The clear and concise presentation in many articles makes this volume suitable for both researchers and graduate students.

Readership

Graduate students and research mathematicians interested in partial differential equations.

Table of Contents

  • L. C. Evans -- Lectures on kinetic formulations of nonlinear PDE
  • C. E. Kenig -- Some recent applications of unique continuation
  • G. Barles and B. Perthame -- Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics
  • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao -- The energy-critical nonlinear Schrödinger equation in \(\mathbb{R}^3\)
  • G. David -- Quasiminimal sets for Hausdorff measures
  • C. E. Kenig, G. Ponce, and L. Vega -- The initial value problem for the general quasi-linear Schrödinger equation
  • A. Petrosyan and H. Shahgholian -- Parabolic obstacle problems applied to finance. A free-boundary-regularity approach
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