Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces

Hongjie Dong; Junhee Ryu

Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces

Analysis of PDEs 2024-04-02 v2

Authors: Hongjie Dong , Junhee Ryu

Abstract

We study nonlocal elliptic and parabolic equations on $C^{1,\tau}$ open sets in weighted Sobolev spaces, where $\tau\in (0,1)$ . The operators we consider are infinitesimal generators of symmetric stable L\'evy processes, whose L\'evy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable.

Keywords

nonlocal elliptic equations nonlocal parabolic equations stable lévy processes weighted sobolev spaces levy measures

Cite

@article{arxiv.2309.05193,
  title  = {Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces},
  author = {Hongjie Dong and Junhee Ryu},
  journal= {arXiv preprint arXiv:2309.05193},
  year   = {2024}
}

Comments

39 pages, minor revision, to appear in SIAM J. Math. Anal

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