TY - JOUR
T1 - Weak Harnack inequality for a mixed local and nonlocal parabolic equation
AU - Garain, Prashanta
AU - Kinnunen, Juha
N1 - Publisher Copyright:
© 2023 The Author(s)
PY - 2023/7/5
Y1 - 2023/7/5
N2 - This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. It is based on energy estimates and the Moser iteration technique. Instead of the parabolic John-Nirenberg lemma, we adopt a lemma of Bombieri-Giusti to the mixed local and nonlocal parabolic case. To this end, we prove an appropriate reverse Hölder inequality and a logarithmic estimate for weak supersolutions.
AB - This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. It is based on energy estimates and the Moser iteration technique. Instead of the parabolic John-Nirenberg lemma, we adopt a lemma of Bombieri-Giusti to the mixed local and nonlocal parabolic case. To this end, we prove an appropriate reverse Hölder inequality and a logarithmic estimate for weak supersolutions.
KW - Energy estimates
KW - Mixed local and nonlocal Laplace operator
KW - Moser iteration
KW - Reverse Hölder inequality
KW - Weak Harnack inequality
UR - http://www.scopus.com/inward/record.url?scp=85149919313&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2023.02.049
DO - 10.1016/j.jde.2023.02.049
M3 - Article
AN - SCOPUS:85149919313
SN - 0022-0396
VL - 360
SP - 373
EP - 406
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -