Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

Qi Xue; Ruofang Yang; Chao Zhang; Qi Xue; Ruofang Yang; Chao Zhang

doi:10.3934/mine.2025029

Mathematics in Engineering

2025, Volume 7, Issue 6: 695-712. doi: 10.3934/mine.2025029

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Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

1.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received: 03 September 2025 Revised: 08 November 2025 Accepted: 24 November 2025 Published: 26 November 2025

In this paper, we aim to establish a new class of weak Harnack inequalities for weak supersolutions to the nonhomogeneous nonlocal equations with general growth. Our approach mainly relies on the expansion of positivity in the spirit of De Giorgi classes, along with a refined energy estimate.
- nonlocal equations,
- weak Harnack estimates,
- general growth
Citation: Qi Xue, Ruofang Yang, Chao Zhang. Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth[J]. Mathematics in Engineering, 2025, 7(6): 695-712. doi: 10.3934/mine.2025029

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Abstract

In this paper, we aim to establish a new class of weak Harnack inequalities for weak supersolutions to the nonhomogeneous nonlocal equations with general growth. Our approach mainly relies on the expansion of positivity in the spirit of De Giorgi classes, along with a refined energy estimate.

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