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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.11747 |
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Table of Contents:
- We consider nonlocal equations of the type \[ (-Δ_{p})^{s}u = μ\quad \text{in }Ω, \] where $Ω\subset \mathbb{R}^{n}$ is either a bounded domain or the whole $\mathbb{R}^{n}$, $μ$ is a Radon measure on $Ω$, $0<s<1$ and $1<p<n/s$. Especially, we extend the existence, regularity and Wolff potential estimates for SOLA (Solutions Obtained as Limits of Approximations), established by Kuusi, Mingione, and Sire (Comm. Math. Phys. 337:1317--1368, 2015), to the strongly singular case $1<p\le2-s/n$. Moreover, using Wolff potentials and Orlicz capacities, we present both a sufficient and a necessary conditions for the existence of SOLA to nonlocal equations of the type \[ (-Δ_{p})^{s}u = P(u) + μ\quad \text{in }Ω, \] where $P(\cdot)$ is either a power function or an exponential function.