On a weighted Trudinger-Moser inequality in RN

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Abreu, Emerson¹  Fernandes Jr, Leandro G.² 

[1] Univ Fed Minas Gerais, ICEx Dept Matemat, Caixa Postal 702, BR-30161970 Belo Horizonte, MG, Brazil

[2] Univ Fed Roraima, Dept Matemat, Av Cap Ene Garcez 2413, BR-69310000 Boa Vista, Parana, Brazil

关键词: Weighted Trudinger-Moser inequality;    Weighted rearrangement;    Schwarz symmetrization;   

DOI  :  10.1016/j.jde.2020.02.023

来源: Elsevier

【 摘 要 】

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type Lu where theta, beta >= 0 and alpha > 0, are constants satisfying some existence conditions. It is worth emphasizing that these operators generalize the p-Laplacianand k-Hessian operators in the radial case. Our results involve fractional dimensions, a new weighted Polya-Szego principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free