L-p MAPPING PROPERTIES FOR NONLOCAL SCHRODINGER OPERATORS WITH CERTAIN POTENTIALS
- Authors
- Choi, Woocheol; Kim, Yong-Cheol
- Issue Date
- 11월-2018
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Nonlocal Schrodinger operator; weak Harnack inequality; fundamental solution
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.38, no.11, pp.5811 - 5834
- Indexed
- SCIE
SCOPUS
- Journal Title
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- Volume
- 38
- Number
- 11
- Start Page
- 5811
- End Page
- 5834
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/72022
- DOI
- 10.3934/dcds.2018253
- ISSN
- 1078-0947
- Abstract
- In this paper, we consider nonlocal Schrodinger equations with certain potentials V is an element of RHq (q > n/2s > 1 and 0 < s < 1) of the form L(K)u Vu = f in R-n where L-K is an integro-differential operator. We denote the solution of the above equation by S-V f := u, which is called the inverse of the nonlocal Schrodinger operator L-K + V with potential V; that is, S-V = (L-K + V)(-1). Then we obtain an improved version of the weak Harnack inequality of non negative weak subsolutions of the nonlocal equation {L(K)u Vu = 0 in Omega, u = g in R-n \ Omega, where g is an element of H-S(R-n) and Omega is a bounded open domain in R-n with Lipschitz boundary, and also get an improved decay of a fundamental solution e(V) for L-K + V. Moreover, we obtain L-p and L-p - L-q mapping properties of the inverse S-V of the nonlocal Schrodinger operator L-K +V.
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