TY - JOUR

T1 - Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains

AU - Bui, The Anh

AU - Duong, Xuan Thinh

PY - 2017

Y1 - 2017

N2 - Consider the nonlinear parabolic equation in the form ut − diva(Du, x, t) = div (|F|p−2F) in Ω × (0, T ), where T > 0 and Ω is a Reifenberg domain. We suppose that the nonlinearity a(ξ, x, t) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity a(ξ, x, t) and to more general setting of Lorentz spaces.

AB - Consider the nonlinear parabolic equation in the form ut − diva(Du, x, t) = div (|F|p−2F) in Ω × (0, T ), where T > 0 and Ω is a Reifenberg domain. We suppose that the nonlinearity a(ξ, x, t) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity a(ξ, x, t) and to more general setting of Lorentz spaces.

UR - http://www.scopus.com/inward/record.url?scp=85015949420&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP140100649

U2 - 10.1007/s00526-017-1130-z

DO - 10.1007/s00526-017-1130-z

M3 - Article

VL - 56

SP - 1

EP - 24

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 2

M1 - 47

ER -