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arXiv · 2509.01941

On boundary H\"{o}lder 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 H\"{o}lder continuous. In the manuscript we consider both the case of ``good'' boundaries and ``domains with prime ends''. We have obtained not only H\"{o}lder-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. 2025-09-02. On boundary H\"{o}lder continuity of Sobolev and Orlicz-Sobolev classes. https://arxiv.org/abs/2509.01941

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