The sliding methods for the fractional p-Laplacian

By Leyun Wu, Wenxiong CHEN *. 2020

86 citations recorded by the source corpus.

Abstract In this paper, we develop a sliding method for the fractional p-Laplacian. We first obtain the key ingredient needed in the sliding method in a bounded domain–the narrow region principle. Then using nonlinear equations involving the fractional p-Laplacian in both bounded domains and in the whole space, we illustrate how this new sliding method can be employed to obtain monotonicity of solutions. During these processes, we introduce a new idea–estimating the singular integrals defining the fractional p-Laplacian along a sequence of approximate maximum points. We believe that the new ideas and methods employed here can be conveniently applied to study a variety of nonlocal problems with more general operators and more general nonlinearities.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ef6c8e3712fc80301ec9dd40901c1e178e48ca0d

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In Applied Mathematics

1. Leyun Wu
2. Wenxiong CHEN *
3. Yahui Niu
4. Yunyun Hu
5. Pengyan Wang
6. Congming LI #
7. Li Ma
8. Yutian Lei

In Computational Theory and Mathematics

1. Leyun Wu
2. Wenxiong CHEN *
3. Yahui Niu
4. Yunyun Hu
5. Pengyan Wang
6. Congming LI #

Citations in the corpus

• Asymptotic method of moving planes for fractional parabolic equations (2020, background): “For elliptic equations involving either local or nonlocal operators, a number of systematic approaches have been established to study these qualitative properties, such as the method of moving planes[8, 20, 21, 27, 33, 34, 35, 45], the method of moving spheres[11, 29], and the sliding methods [15, 1”
• Liouville Theorems for Fractional Parabolic Equations (2021, methodology): “To this end, a number of systematic approaches have been established, such as the extension method ([7]), the method of moving planes ([2, 4, 9, 10, 23]), the method of moving spheres ([11, 29]), and the sliding methods ([3, 39]).”