具有 $p$-可积扭曲的映射的雅可比行列式倒数的全局可积性
Global Integrability of the Reciprocal of Jacobians for Homeomorphisms of Finite Distortion
AI总结：
研究了有限扭曲映射雅可比行列式倒数的全局可积性，并加强了关于弱极限的 Sobolev 映射结果。
摘要：
对于具有 $p$-可积扭曲的映射，我们获得了其雅可比行列式倒数的最佳全局可积性程度。作为应用，我们加强了 Doležalová、Hencl 和 Malý 关于有限扭曲的 Sobolev 映射弱极限结果。这些极限代表了物理上可接受的变形，因为它们几乎处处保持单射性，因此尽可能符合数学非线性弹性模型中物质不穿透原理。
英文摘要：
For a homeomorphism with $p$-integrable distortion, we obtain the optimal global degree of integrability for the reciprocal of its Jacobian determinant. As an application, we strengthen the result of Doležalová, Hencl and Malý concerning weak limits of Sobolev homeomorphisms with finite distortion. Such limits represent physically admissible deformations, as they remain injective almost everywhere and thus adhere as closely as possible to the principle of non-interpenetration of matter in mathematical models of nonlinear elasticity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
