Sobolev inequality with non-uniformly degenerating gradient

IF 1.1 4区数学 Q1 MATHEMATICS

Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2022-01-01 DOI:10.14232/ejqtde.2022.1.24

F. Mamedov, S. Monsurrò

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引用次数: 1

Abstract

In this paper we prove the following weighted Sobolev inequality in a bounded domain Ω ⊂ R n , n ≥ 1 , of a homogeneous space ( R n , ρ , w d x ) , under suitable compatibility conditions on the positive weight functions ( v , w , ω 1 , ω 2 , … , ω n ) and on the quasi-metric ρ , ( ∫ Ω | f | q v w d z ) 1 q ≤ C ∑ i = 1 N ( ∫ Ω | f z i | p ω i M S w d z ) 1 p , f ∈ L i p 0 ( Ω ¯ ) , where q ≥ p > 1 and M S denotes the strong maximal operator. Some corollaries on non-uniformly degenerating gradient inequalities are derived.

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具有非一致退化梯度的Sobolev不等式

本文证明了齐次空间(rn， ρ， wdx)的有界域Ω∧R n, n≥1上的下列加权Sobolev不等式，在合适的相容条件下，正权函数(v, w， Ω 1， Ω 2，…，Ω n)和拟度量ρ，(∫Ω | f | q v w d z) 1 q≤C∑i = 1 N(∫Ω | f z i | p Ω i M S w d z) 1 p, f∈L i p 0 (Ω¯)，式中q≥p >1, ms为强极大算子。给出了非一致退化梯度不等式的若干推论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Journal of Qualitative Theory of Differential Equations 数学-数学

CiteScore

1.40

自引率

9.10%

发文量

审稿时长

3 months

期刊介绍： The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875. All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.