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Sobolev mappings with integrable dilatations

✍ Scribed by Juha Heinonen; Pekka Koskela

Book ID
104763058
Publisher
Springer
Year
1993
Tongue
English
Weight
853 KB
Volume
125
Category
Article
ISSN
0003-9527

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✦ Synopsis

We show that each quasi-light mapping fin the Sobolev space W~'n(s R n) satisfying ]Df(x)ln<=K(x,f)J(x,f) for almost every x and for some K~Lr(s r > n-1, is open and discrete. The assumption that f be quasilight can be dropped if, in addition, it is required that f~ WI'P(f2, R n) for some p ___ n + 1/(n -2). More generally, we consider mappings in the John Ball classes dp, q(s and give conditions that guarantee their discreteness and openness.

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## Abstract We consider the Sobolev spaces of square integrable functions __v__, from ℝ^__n__^ or from one of its hyperquadrants __Q__, into a complex separable Hilbert space, with square integrable sum of derivatives βˆ‘βˆ‚~__𝓁__~__v__. In these spaces we define closed trace operators on the boundarie