Concentration-compactness principle associated with Adams' inequality in Lorentz-Sobolev space

نویسندگان

چکیده

Abstract The concentration-compactness principle of Lions type in Euclidean space relies on the Pólya-Szegö inequality, which is not available non-Euclidean settings. first proof setting, such as Heisenberg group, was given by Li et al. using a symmetrization-free nonsmooth truncation argument. In this article, we study second-order Adams’ inequality Lorentz-Sobolev W 0 2 L , q ( ? stretchy="false">) {W}_{0}^{2}{L}^{2,q}(\Omega ) for all 1 < ? 1\lt q\lt \infty . Due to absence with respect derivatives, will use argument space. Furthermore, show sharpness result constructing test function sequence. Our even new first-order case when > q\gt 2

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ژورنال

عنوان ژورنال: Advanced Nonlinear Studies

سال: 2022

ISSN: ['1536-1365', '2169-0375']

DOI: https://doi.org/10.1515/ans-2022-0043