具有迪里夏特条件的分数 p-拉普拉奇的最优可解性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-09-13 DOI:10.1007/s13540-024-00341-w

Antonio Iannizzotto, Dimitri Mugnai

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引用次数: 0

摘要

我们研究了一个由分数 p-Laplacian 驱动的非线性、非局部 Dirichlet 问题，其中涉及一个（(p-1)\）次线性反应。通过弱比较原理，我们证明了解的唯一性。同时，通过将该问题与同一算子的 "渐近 "加权特征值问题进行比较，我们证明了解存在的必要条件和充分条件。我们的研究将 Brezis-Oswald [7] 和 Diaz-Saa [11] 的经典结果扩展到了非线性非局部框架。

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Optimal solvability for the fractional p-Laplacian with Dirichlet conditions

We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a \((p-1)\)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464