A Logarithmic Weighted Adams-type inequality in the whole of ℝ^N with an application

2023/11/28 by Jaidane, Rached
#$35$J$20$ #$35$J$30$ #$35$J$60$ #$35$K$57$ #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.16786

Abstract

In this paper, we will establish a logarithmic weighted Adams inequality in a logarithmic weighted second order Sobolev space in the whole set of ℝ^N. Using this result, we delve into the analysis of a weighted fourth-order equation in ℝ^N. We assume that the non-linearity of the equation exhibits either critical or subcritical exponential growth, consistent with the Adams-type inequalities previously established. By applying the Mountain Pass Theorem, we demonstrate the existence of a weak solution to this problem. The primary challenge lies in the lack of compactness in the energy caused by the critical exponential growth of the non-linear term f.

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