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Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces
Donatella Danielli
Nicola Garofalo
Duy-Minh Nhieu
出版
American Mathematical Soc.
, 2006
主題
Mathematics / General
Mathematics / Algebra / General
Mathematics / Calculus
Mathematics / Differential Equations / Partial
Mathematics / Infinity
Mathematics / Mathematical Analysis
Mathematics / Functional Analysis
ISBN
082183911X
9780821839119
URL
http://books.google.com.hk/books?id=pQTTAQAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
The object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Caratheodory space. Such traces are defined in terms of suitable Besov spaces with respect to a measure which is concentrated on a lower dimensional manifold, and which satisfies an Ahlfors type condition with respect to the standard Lebesgue measure. We also study the extension problem for the relevant Besov spaces. Various concrete applications to the setting of Carnot groups are analyzed in detail and an application to the solvability of the subelliptic Neumann problem is presented.