Some remarks about the summability of nonlocal nonlinear problems

Advances in Nonlinear Analysis

article

Begoña Barrios¹  Ireneo Peral¹  Stefano Vita² 

[1] Universidad Autonoma de Madrid;Dipartimento di Matematica “Giuseppe Peano”

关键词: p-fractional Laplacian;    Stampacchia's method;    Moser's method;    Calderón–Zygmund summability result;   

DOI  :  10.1515/anona-2015-0012

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this note, we will study the problem (-Δ) p s u = f ( x ) on Ω, u = 0 in ℝ N ∖Ω, where 0 < s < 1, (-Δ) p s 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.

【 授权许可】

CC BY