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Recent Trends in Nonlinear Partial Differential Equations I: Evolution Problems
Edited by: James B. Serrin, Enzo L. Mitidieri, University of Trieste, Italy, and Vicenţiu D. Rădulescu, University of Craiova, Romania
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Contemporary Mathematics
2013; 307 pp; softcover
Volume: 594
ISBN-10: 0-8218-8736-X
ISBN-13: 978-0-8218-8736-3
List Price: US$111
Member Price: US$88.80
Order Code: CONM/594
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This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday.

The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide ranging influence of Professor Pucci on the field of nonlinear analysis and partial differential equations.

In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

The companion volume (Contemporary Mathematics, Volume 595) is devoted to stationary problems in nonlinear partial differential equations.

Readership

Graduate students and research mathematicians interested in nonlinear partial differential equations.

Table of Contents

  • J. Mawhin -- A tribute to Patrizia Pucci
  • G. Vinti -- A scientific profile of Patrizia Pucci
  • J. Serrin -- The Liouville theorem for homogeneous elliptic differential inequalities
  • B. Abdellaoui, I. Peral, and M. Walias -- Multiplicity results for porous media and fast diffusion equations with a quadratic gradient term
  • G. Autuori -- A priori estimates for solutions of \(p\)-Kirchhoff systems under dynamic boundary conditions
  • G. Barbatis and F. Gazzola -- Higher order linear parabolic equations
  • N. Bellomo and V. Coscia -- Sources of nonlinearity in the kinetic theory for active particles with focus on the formation of political opinions
  • B. Bianchini, L. Mari, and M. Rigoli -- Yamabe type equations with sign-changing nonlinearities on the Heisenberg group, and the role of Green functions
  • M. Chipot and K. Yeressian -- Asymptotic behavior of the solution to variational inequalities with joint constraints on its value and its gradient
  • F. Colasuonno and M. C. Salvatori -- Existence and uniqueness of solutions to a Cauchy problem modeling the dynamics of socio-political conflicts
  • F. Farroni, R. Giova, and C. Sbordone -- Regularity points of ACL-homeomorphisms in the plane
  • S. Fornaro, M. Sosio, and V. Vespri -- Energy estimates and integral Harnack inequality for some doubly nonlinear singular parabolic equations
  • K. T. Gkikas and L. Véron -- Initial value problems for diffusion equations with singular potential
  • E. Lanconelli and A. Montanari -- On a class of fully nonlinear PDEs from complex geometry
  • A. Malchiodi -- Concentration of conformal volume, improved Moser-Trudinger inequalities and Toda systems
  • J. Mawhin -- Periodic solutions of Lagrangian difference systems: Periodic nonlinearities (almost) don't matter
  • D. Mugnai -- A limit problem for degenerate quasilinear variational inequalities in cylinders
  • E. Vitillaro -- Strong solutions for the wave equation with a kinetic boundary condition
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