Open AccessRegularity results of solutions to elliptic equations involving mixed local and nonlocal operators
Author(s) -
CaiDan LaMao,
AUTHOR_ID,
Shuibo Huang,
Qiaoyu Tian,
Can-Yun Huang,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022233
Subject(s) - bounded function , omega , domain (mathematical analysis) , mathematics , elliptic operator , operator (biology) , matrix (chemical analysis) , combinatorics , physics , mathematical analysis , chemistry , quantum mechanics , biochemistry , repressor , chromatography , transcription factor , gene
In this paper, we study the summability of solutions to the following semilinear elliptic equations involving mixed local and nonlocal operators \begin{document}$ \left\{ \begin{matrix} - \Delta u(x)+{{(-\Delta )}^{s}}u(x)=f(x), & x\in \Omega , \\ u(x)\ge 0, & x\in \Omega , \\ u(x)=0, & x\in {{\mathbb{R}}^{N}}\setminus \Omega , \\\end{matrix} \right. $\end{document} where $ 0 < s < 1 $, $ \Omega\subset \mathbb{R}^N $ is a smooth bounded domain, $ (-\Delta)^s $ is the fractional Laplace operator, $ f $ is a measurable function.