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The book is an account on recent advances in elliptic and parabolic problems and related equations, including general quasi-linear equations, variational structures, Bose-Einstein condensate, Chern-Simons model, geometric shell theory and stability in fluids. It presents very up-to-date research on central issues of these problems such as maximal regularity, bubbling, blowing-up, bifurcation of solutions and wave interaction. The contributors are well known leading mathematicians and prominent young researchers. The proceedings have been selected for coverage in:. Index to Scientific & Techn
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Dieses zweibändige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen,parabolischen und hyperbolischen Typ - in zwei und mehreren Veränderlichen vor. Im vorliegenden zweiten Band werden folgende Themen behandelt: Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, Schaudersche Theorie linearer elliptischer Differentialgleichungen, schwache Lösungen elliptischer Differentialgleichungen, nichtlineare partielle Differentialgleichungen und Charakteristikentheorie, nichtlineare elliptische Systeme mit differentialgeometrischen Anwendungen. Während im vorausgehenden Band die partiellen Differentialgleichungen mit Integraldarstellungen im Mittelpunkt standen, werden nun funktionalanalytische Lösungsmethoden vorgestellt. Dieses Lehrbuch kann daher für einen mehrsemestrigen Kurs verwendet werden. Fortgeschrittene Leser können jedes Kapitel auch unabhängig voneinander studieren.
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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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