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Nonlocal Harnack inequalities for nonlocal heat equations
- Authors
- Kim, Yong-Cheol
- Issue Date
- 15-11월-2019
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, v.267, no.11, pp.6691 - 6757
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF DIFFERENTIAL EQUATIONS
- Volume
- 267
- Number
- 11
- Start Page
- 6691
- End Page
- 6757
- ISSN
- 0022-0396
- Abstract
- By applying the De Giorgi-Nash-Moser theory, we obtain nonlocal Harnack inequalities for locally non-negative weak solutions of nonlocal parabolic equations given by an integro-differential operator L-K as follows: {L(K)u + partial derivative(t)u = 0 in Omega(I) := Omega x (-T, 0] u = g in partial derivative(p)Omega(I) : = ((R-n\Omega) x (-T, 0]) boolean OR(Omega x {t = -T}) for g is an element of C(R-I*(n)) boolean AND L-infinity (R-n x (-T, 0]) boolean AND H-T(s)(R-n) and a bounded domain Omega subset of R-n with Lipschitz boundary. Interestingly, this result implies the classical Harnack inequalities for globally nonnegative weak solutions. (C) 2019 Elsevier Inc. All rights reserved.
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