## Elliptic and Parabolic Problems: A Special Tribute to the Work of Haim Brezis (Google eBook)Catherine Bandle, Henri Berestycki, Bernhard Brighi, Alain Brillard, Michel Chipot, Jean-Michel Coron, Carlo Sbordone, Itai Shafrir, Vanda Valente, Giorgio Vergara Caffarelli The goal of these proceedings and of the meeting of Gaeta was to celebrate and honor the mathematical achievements of Haim Brezis. The prodigious in?uence of histalentandhispersonalityinthedomainofnonlinearanalysisisunanimously- claimed!This impactis visible inthe huge number ofhis formerstudents (dozens), students of former students (hundreds) and collaborators (hundreds). Thus the Gaeta meeting was, to some extent, the family reunion of part of this large c- munity sharing a joint interest in the ?eld of elliptic and parabolic equations and pushing it to a very high standard. Italyhasa longtraditionandtasteforanalysisandwecouldnot?ndabetter placeneitheramorecompletesupportfortherealisationofourproject.Wehaveto thank here the university of Cassino, Napoli, Roma “la Sapienza”, the GNAMPA- Istituto di Alta Matematica, CNR-IAC, MEMOMAT, RTN Fronts-Singularities, the commune of Gaeta. Additional founding came from the universities of M- house and Zur ̈ ich. Finally, we are grateful to Birkh ̈ auser and Dr. Hemp?ing who allowed us to record the talks of this conference in a prestigious volume. The organizers Progress in Nonlinear Di?erential Equations and Their Applications, Vol. 63, 1–12 c 2005 Birkh ̈ auser Verlag Basel/Switzerland One-Layer Free Boundary Problems with Two Free Boundaries Andrew Acker Abstract. We studythe uniquenessand successive approximation of solutions of a class of two-dimensional steady-state ?uid problems involving in?nite periodic ?ows between two periodic free boundaries, each characterized by a ?ow-speed condition related to Bernoulli’s law. |

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### Contents

13 | |

A Bermúdez R Leira M C Muniz and F Pena | 33 |

Betelú M A Fontelos and U Kindelán | 51 |

Lucio Boccardo | 67 |

Bernard Brighi and JeanDavid Hoernel | 83 |

A Canada J A Montero and S Villegas | 103 |

A Canada and D Ruiz | 111 |

Ana Carpio | 127 |

Jérôme Droniou | 235 |

Alberto Fiorenza | 259 |

Thierry Gallouët | 279 |

Mohammed Guedda | 298 |

S Kamin H Berestycki L Kagan and G Sivashinsky | 319 |

Jean Mawhin | 342 |

Sergio Polidoro | 365 |

Vicentiu Radulescu | 389 |

Michel Chipot and Yitian | 147 |

Comte | 173 |

Juan Dávila and Marcelo Montenegro | 189 |

U De Maio and T A Melnyk | 207 |

Marc Oliver Rieger | 402 |

Valente | 423 |

Laurent Véron | 453 |

### Common terms and phrases

2005 Birkhäuser Verlag algorithm Anal Appl Applications approximation assume assumption asymptotic behavior Birkhäuser Verlag Basel/Switzerland blow-up boundary conditions boundary value problem Brezis Cantor set coagulation coefficients compact compact support computation consider control system convergence convex D´ıaz deﬁned deﬁnition denote differential equations dimension Dirichlet e-mail elliptic equations elliptic problems energy estimates exists finite ﬁrst fractal fragmentation equation free boundary function given global Harnack inequality integral Lagrangian large solution Lemma linear Math Mathematics Mathematics Subject Classification maximum principle mesh method metric minimizers monotone Moreover nonlinear nonlinear elliptic numerical obtain operator parabolic partial differential equations PDEs porous medium positive constant proof of Theorem Proposition proved Radon measure regularity satisﬁes satisfying Section self-similar semilinear sequence similar solutions singular Sobolev space subset theory Wasserstein metrics wave fronts weak solution Young measures