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UID:8283@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20141007T110000
DTEND;TZID=Europe/Paris:20141007T120000
DTSTAMP:20241120T210323Z
URL:https://www.i2m.univ-amu.fr/evenements/weighted-sobolev-spaces-on-weig
 hted-metric-measure-spaces/
SUMMARY: (...): Weighted Sobolev Spaces on Weighted Metric Measure Spaces
DESCRIPTION:: We investigate weighted Sobolev spaces on metric measure spac
 es $(X\, d\, m)$. Denoting by $\\rho$ the weight function\, we compare the
  space $W^{1\,p} (X\, d\, \\rho m)$ (which always concides with the closur
 e $H^{1\,p} (X\, d\, \\rho m)$ of Lipschitz functions) with the weighted S
 obolev spaces $W_{\\rho}^{1\,p} (X\, d\, m)$ and $H_{\\rho}^{1\,p} (X\, d\
 ,m)$ defined as in the Euclidean theory of weighted Sobolev spaces. Under 
 mild assumptions on the metric measure structure and on the weight we show
  that $W^{1\,p}(X\, d\, \\rho m) = H_{\\rho}^{1\,p} (X\, d\, m)$. We also 
 adapt the results proved by Muckenhoupt and the ones proved by Zhikov to t
 he metric measure setting\, considering appropriate conditions on $\\rho$ 
 that ensure the equality $W_{\\rho}^{1\,p} (X\, d\, m) =H_{\\rho}^{1\,p} (
 X\, d\, m)$. This is a joint work with Luigi Ambrosio and Gareth Speight.\
 nAndrea Pinamonti\, Università di Trento\n\n
CATEGORIES:Séminaire,Analyse Appliquée
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