Work

Fractional elliptic and parabolic equations-Liouville theorems, regularities, and a priori estimates

Year: 2025

Type: article

Abstract: In this paper, we present a summary of our recent advancements in the study of various fractional elliptic and parabolic equations, with a focus on Liouville type theorems, integral representations of solutions, interior regularities, blow-up and re-scaling analysis, and a priori estimates.These results and their proofs have been previously published in various sources. Here, we adopt an intuitive approach, using clear language and visual illustrations to highlight the inner connections among these results and the ideas behind their proofs. Our goal is to provide readers with a comprehensive understanding of these approaches, enabling them to effectively apply the useful methods to solve a wide range of related problems in this field.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2025069

Authors: Wenxiong Chen, Yahong Guo

Institutions: Yeshiva University, Shanghai Jiao Tong University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Awards: G3735139270, G3746359664, G5497088379