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New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $$ {\mathbb {R}}^N $$ R N and applications
Calculus of Variations and Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-02-05 , DOI: 10.1007/s00526-021-01925-7
Sami Aouaoui , Rahma Jlel

In this paper, we provide an extension to the whole euclidean space \( {\mathbb {R}}^N,\ N \ge 2, \) of the Trudinger–Moser inequalities proved by Calanchi and Ruf (Nonlinear Anal 121:403–411, 2015) involving a logarithmic weight. The inequalities are new and highlight very well the importance of the presence of this type of weight. Next, we prove some version of the concentration-compactness principle due to P.L. Lions giving some new improvements of the Trudinger–Moser inequalities established in the first part of this work. In the light of this last result, we treat some elliptic quasilinear problems involving new type of exponential growth condition at infinity.



中文翻译:

在整个欧几里德空间上定义的新的加权锐化Trudinger-Moser不等式$$ {\ mathbb {R}} ^ N $$ RN及其应用

在本文中,我们提供了由Calanchi和Ruf证明的Trudinger-Moser不等式的整个欧氏空间\({\ mathbb {R}} ^ N,\ N \ ge 2 \)(非线性肛门121:403) –411,2015年)涉及对数权重。这种不平等是新的,并且很好地突出了这种重量存在的重要性。接下来,由于PL Lions对本文第一部分中建立的Trudinger-Moser不等式进行了一些新的改进,因此我们证明了浓度紧致性原理的某种形式。根据最后的结果,我们处理了一些椭圆的拟线性问题,这些问题涉及无穷大时新型的指数增长条件。

更新日期:2021-02-07
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