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arXiv · 1604.00058

Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces

Ariel Barton
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Abstract

There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain U to functions in a Besov space on the boundary bU. We extend these theorems to the case where the Sobolev exponent p is less than one by modifying our Sobolev spaces to consider averages of functions in Whitney balls. Averaged Sobolev spaces are also of interest in the applications in the case where p>1, and so we also provide trace and extension results in that case. Finally, we provide some comparable results for Neumann traces and extensions.

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Ariel Barton. 2016-03-31. Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces. https://arxiv.org/abs/1604.00058

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