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Paper detail

Composition operators on Sobolev spaces and Ball's classes

In this paper we study geometric aspects of Ball's classes in the context of nonlinear elasticity problems. The suggested approach is based on the characterization of Ball's classes $A_{q,q'}(Ω)$ in terms of composition operators on Sobolev spaces. This characterization allows us to obtain the volume compression (distortion) estimates of topological mappings of Ball's classes. We prove also that Sobolev homeomorphisms of Ball's classes which possess the Luzin $N$-property are absolutely continuous with respect to capacity.

preprint2022arXivOpen access
Vladimir Gol'dshteinAlexander Ukhlov
math.AP
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Vladimir Gol'dshteinAlexander Ukhlov

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