Some remarks about the summability of nonlocal nonlinear problems
Some remarks about the summability of nonlocal nonlinear problems
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DOI：
10.1515/anona-2015-0012
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发表时间：
2015-05
影响因子：
4.2
通讯作者：
B. Barrios;I. Peral;S. Vita
中科院分区：
文献类型：
--
作者：
B. Barrios;I. Peral;S. Vita
本文研究了Ω上的（-Δ）ps u = f（x），u = 0，其中0 < s < 1，（-Δ）ps是下面定义的非局部p-Laplacian，Ω是光滑有界区域.在这项工作中研究的要点是证明，适应中使用的技术[`基本估计的椭圆和抛物方程的解一类非局部算子'，离散连续。Dyn.系统：对于p = 2到p ∈（1，+∞）的一般情形，有限能量解的可和性是由源项f（x）的可和性给出的.本说明的目的是以尽可能基本的方式介绍结果。
Abstract In this note, we will study the problem (-Δ)ps u = f(x) on Ω, u = 0 in ℝN∖Ω, where 0 < s < 1, (-Δ)ps is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [`Basic estimates for solution of elliptic and parabolic equations for a class of nonlocal operators', Discrete Contin. Dyn. Syst., to appear] for the case p = 2 to the general case p ∈ (1, +∞), the summability of the finite energy solutions in terms of the summability of a source term f(x). The aim of this note is to present the results in a way as elementary as possible.