PDE AS A UNIFIED SUBJECT

• cours - matière potentielle : to the articial distinctions

GAFA Geom funct anal Special Volume GAFA X c Birkhauser Verlag Basel GAFA Geometric And Functional Analysis PDE AS A UNIFIED SUBJECT Sergiu Klainerman Introduction Given that one of the goals of the conference is to address the issue of the unity of Mathematics I feel emboldened to talk about a question which has kept bothering me all through my scientic career Is there really a unied subject of Mathematics which one can call PDE At rst glance this seems easy we may dene PDE as the subject which is concerned with all partial dierential equations According to this view the goal of the subject is to nd a general theory of all or very general classes of PDEs This natural

• linear theory
• range of applications of specic pdes
• general framework
• complex analysis
• nonlinear evolution equations
• pdes
• solutions
• equations
• subject
• problem