On one variant of strongly nonlinear Gagliardo-Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems

被引：0
|
作者：
Choczewski T. [1 ]
Kalamajska A. [1 ,2 ]
机构：
[1] Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, Warsaw
[2] Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, Warsaw
来源：
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni | 2019年 / 30卷 / 03期
关键词：
Elliptic PDE's; Gagliardo-Nirenberg inequalities; Interpolation inequalities; Regularity; Sobolev spaces;
D O I：
10.4171/RLM/855
中图分类号：
学科分类号：
摘要：
We obtain the inequality (Equation Presented) where Ω ⊂ Rn is a bounded Lipschitz domain, u ∈ W2; 1 loc (Ω) is positive and obeys some additional assumptions, Δu is the Laplace operator, Th;C( ) is certain transformation of the continuous function h( ). We also explain how to apply such inequality to deduce regularity for solutions of nonlinear eigenvalue problems of elliptic type for degenerated PDEs, with the illustration within the model of electrostatic micromechanical systems (MEMS). © 2019 European Mathematical Society Publishing House. All rights reserved.
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页码：479 / 496
页数：17
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