低维情形下的拟线性 Brezis-Nirenberg 问题
偏微分方程分析
2023-04-28 v1
摘要
我们讨论了低维情形下具有临界 Sobolev 增长的拟线性椭圆方程 [H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437--477; M. Guedda, L. Veron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. 13 (1989), no. 8, 879--902] 的存在性结果，其中该问题具有全局特征，正如 [O. Druet, Elliptic equations with critical Sobolev exponents in dimension 3, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 19 (2002), no. 2, 125--142; P. Esposito, On some conjectures proposed by Ha"im Brezis, Nonlinear Anal. 54 (2004), no. 5, 751--759] 中那样，该特征编码于相应 Green 函数“正则”部分符号性质中。
引用
@article{arxiv.2304.14215,
title = {The quasi-linear Brezis-Nirenberg problem in low dimensions},
author = {Sabina Angeloni and Pierpaolo Esposito},
journal= {arXiv preprint arXiv:2304.14215},
year = {2023}
}
备注
arXiv admin note: substantial text overlap with arXiv:2203.01206