As we all know, every holder continuous function is Bounded and uniform continuity in domain $\omega$. Now we give a more large domain $X$, then $\omega \subset \subset X$. Can we find a extension operator $E$ that makes $Eu|_\omega=u,$ $Eu$ is holder continuous function in the larger domain $X$? If the general situation does not work, especially, $\omega$ is bounded?
2026-03-25 12:21:26.1774441286
Holder Extension Operator
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