无界域上嵌入结果与分数$p(x,.)$-\ Laplacian 问题
偏微分方程分析
2025-09-03 v1
摘要
In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems driven by the fractional -Laplacian operator. Using variational methods combined with the established embedding result, we prove the existence of nontrivial weak solutions under suitable growth and regularity conditions on the nonlinearity.\ A significant analytical challenge addressed in this work arises from both the nonlocal behavior of the fractional -Laplacian and the lack of compactness induced by the unboundedness of the domain.
引用
@article{arxiv.2509.01783,
title = {Embedding Results and Fractional $p(x,.)$-Laplacian Problem in Unbounded Domains},
author = {Abdelkrim Barbara and Ahmed Bousmaha and Mohammed Shimi},
journal= {arXiv preprint arXiv:2509.01783},
year = {2025}
}