Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth

2023/11/02 by Kim, Minhyun, Lee, Se-Chan · 4 citations
#31B05 #31B25 #35R09 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.01246

Abstract

We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal nonlinear potential theory. We provide several fine properties of supersolutions and superharmonic functions, and reveal the relation between them. Along the way we prove some results for nonlocal obstacle problems such as the well-posedness and (both interior and boundary) regularity estimates, which are of independent interest.

Cited by

• Nonlocal Harnack inequality in a disconnected region
• Fractional sublinear Sobolev inequality for L-superharmonic functions
• Liouville theorem for singular solutions to nonlocal equations
• Semiregular and strongly irregular boundary points for nonlocal Dirichlet problems

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