Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients

The Anh Bui; Xuan Thinh Duong

doi:10.2422/2036-2145.201608_003

Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients

The Anh Bui, Xuan Thinh Duong

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Consider the parabolic equation with measure data (Equation Presented) where Ω is a bounded domain in Rⁿ, Ω_T = Ω × (0, T), ∂_pΩ_T = (∂Ω × (0, T))U (Ω × {0}), and μ is a signed Borel measure with finite total mass. Assume that the nonlinearity a satisfies a small BMO-seminorm condition, and Ω is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.

Original language	English
Pages (from-to)	881-916
Number of pages	36
Journal	Annali della Scuola normale superiore di Pisa - Classe di scienze
Volume	18
Issue number	3
DOIs	https://doi.org/10.2422/2036-2145.201608_003
Publication status	Published - 1 Jan 2018

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abstract = "Consider the parabolic equation with measure data (Equation Presented) where Ω is a bounded domain in Rn, ΩT = Ω × (0, T), ∂pΩT = (∂Ω × (0, T))U (Ω × \{0\}), and μ is a signed Borel measure with finite total mass. Assume that the nonlinearity a satisfies a small BMO-seminorm condition, and Ω is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.",

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T1 - Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients

AU - Bui, The Anh

AU - Duong, Xuan Thinh

PY - 2018/1/1

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N2 - Consider the parabolic equation with measure data (Equation Presented) where Ω is a bounded domain in Rn, ΩT = Ω × (0, T), ∂pΩT = (∂Ω × (0, T))U (Ω × {0}), and μ is a signed Borel measure with finite total mass. Assume that the nonlinearity a satisfies a small BMO-seminorm condition, and Ω is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.

AB - Consider the parabolic equation with measure data (Equation Presented) where Ω is a bounded domain in Rn, ΩT = Ω × (0, T), ∂pΩT = (∂Ω × (0, T))U (Ω × {0}), and μ is a signed Borel measure with finite total mass. Assume that the nonlinearity a satisfies a small BMO-seminorm condition, and Ω is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.

UR - https://www.scopus.com/pages/publications/85051861766

U2 - 10.2422/2036-2145.201608_003

DO - 10.2422/2036-2145.201608_003

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JO - Annali della Scuola normale superiore di Pisa - Classe di scienze

JF - Annali della Scuola normale superiore di Pisa - Classe di scienze

IS - 3

ER -

Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients

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