A linear boundary value problem for weakly quasiregular mappings in space |
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Authors: | Baisheng Yan |
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Institution: | (1) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA (e-mail: yan@math.msu.edu), US |
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Abstract: | Given a number a weakly L-quasiregular map on a domain in space is a map u in a Sobolev space that satisfies almost everywhere in In this paper, we study the problem concerning linear boundary values of weakly L-quasiregular mappings in space with dimension It turns out this problem depends on the power p of the underlying Sobolev space. For p not too far below the dimension n we show that a weakly quasiregular map in can only assume a quasiregular linear boundary value; however, for all and , we prove a rather surprising existence result that every linear map can be the boundary value of a weakly L-quasiregular map in
Received July 20, 2000 / Accepted September 22, 2000 / Published online December 8, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 30C65 30C70 35F30 49J30 |
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