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UID:6033@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220524T110000
DTEND;TZID=Europe/Paris:20220524T120000
DTSTAMP:20241120T200722Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-12/
SUMMARY:Azahara DeLaTorre Pedraza (Sapienza Università di Roma. ): From Co
 nformal Geometry to the study of non-local semilinear elliptic PDEs
DESCRIPTION:Azahara DeLaTorre Pedraza: \n\nThe so called Yamabe problem in 
 Conformal Geometry consists in finding a metric conformal to a given one a
 nd which has constant scalar curvature. From the analytic point of view\, 
 this problem becomes a semilinear elliptic PDE with critical (for the Sobo
 lev embedding) power non-linearity. If we study the problem in the Euclide
 an space\, allowing the presence of nonzero-dimensional singularities can 
 be transformed into reducing the non-linearity to a Sobolev-subcritical po
 wer. A quite recent notion of non-local curvature gives rise to a parallel
  study which weakens the geometric assumptions giving rise to a non-local 
 semilinear elliptic PDE.\n\nIn this talk\, we will focus on the study of t
 he solutions of these non-local (or fractional) semilinear elliptic PDEs w
 hich represent metrics which are singular along nonzero-dimensional singul
 arities. In collaboration with Ao\, Chan\, Fontelos\, González and Wei\, 
 we covered the construction of solutions which are singular along (zero an
 d positive dimensional) smooth submanifolds. This was done through the dev
 elopment of new methods coming from conformal geometry and Scattering theo
 ry for the study of non-local ODEs. Due to the limitations of the techniqu
 es we used\, the particular case of ``maximal’’ dimension for the sing
 ularity was not covered. In a recent work\, in collaboration with H. Chan\
 , we covered this specific dimension constructing and studying singular so
 lutions of critical dimension. This was done through the study of the Lane
 -Emden-Serrin equation.\n\n\n\n\n
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage)\
 , 39 Rue Joliot Curie\, 13013 Marseille\, France\, Campus Château-Gombert
 \, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=39 Rue Joliot Curie\, 13013
  Marseille\, France\, Campus Château-Gombert\, ;X-APPLE-RADIUS=100;X-TITL
 E=I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage):geo:0,
 0
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