Anisotropic fractional Sobolev extension and its applications
Tóm tắt
In this paper, we show that every function in an anisotropic fractional Sobolev space defined on a regular domain extends to a function defined on the whole
$${\mathbb {R}}^n$$
with the same Sobolev indices. As an application, we get that such functions are Hölder continuous and we give an explicit estimate for the continuity exponent.
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