非光滑域上具有矩阵权重和可测非线性的椭圆方程

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-05-11 DOI:10.1090/proc/16770

Sun-Sig Byun, Yumi Cho, Ho-Sik Lee

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引用次数: 0

摘要

我们研究了在非光滑有界域上具有奇异/退化矩阵权重和可测非线性的一般椭圆方程，在矩阵权重的对数具有较小的有界均值振荡（BMO）规范、允许非线性仅在一个变量中可测量但在其他变量中具有较小的 BMO 规范以及域的边界在 Reifenberg 意义上足够平坦等可能最小的假设条件下，获得了全局 Calderón-Zygmund 类型估计。

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Elliptic equations with matrix weights and measurable nonlinearities on nonsmooth domains

We study general elliptic equations with singular/degenerate matrix weights and measurable nonlinearities on nonsmooth bounded domains to obtain a global Calderón-Zygmund type estimate under possibly minimal assumptions that the logarithm of the matrix weight has a small bounded mean oscillation (BMO) norm, the nonlinearity is allowed to be merely measurable in one variable but has a small BMO norm in the other variables and that the boundary of the domain is sufficiently flat in Reifenberg sense.

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.