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arXiv · 2509.01941

On boundary Hölder continuity of Sobolev and Orlicz-Sobolev classes

Victoria Desyatka·Zarina Kovba·Evgeny Sevost'yanov
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Abstract

We investigate distortion estimates for mappings at boundary points of a domain. We consider mappings of the Sobolev and Orlicz-Sobolev classes and some other classes of mappings that do not preserve the boundary of a domain. For above mappings, we establish distortion estimates at boundary points. In particular, under certain conditions on the characteristics of the mappings, we show that they are Hölder continuous. In the manuscript we consider both the case of ``good'' boundaries and ``domains with prime ends''. We have obtained not only Hölder-type estimates, but also some more general ones under appropriate (more general) conditions on the characteristic.

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Victoria Desyatka, Zarina Kovba, Evgeny Sevost'yanov. 2026-03-15. On boundary Hölder continuity of Sobolev and Orlicz-Sobolev classes. https://arxiv.org/abs/2509.01941

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