Boundary riesz potential estimates for parabolic equations with measurable nonlinearities

Ho Sik Lee; Youchan Kim

doi:10.3934/cam.2025004

Boundary riesz potential estimates for parabolic equations with measurable nonlinearities

Ho Sik Lee
, Youchan Kim

Department of Mathematics

Bielefeld University

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

Abstract

We obtain a boundary pointwise gradient estimate on a parabolic half cube Q₂_R ∩{(x¹, x', t) є Rⁿ⁺¹: X¹ > 0} for nonlinear parabolic equations with measurable nonlinearities, which are only assumed to be measurable in x¹-variable. The estimates are obtained in terms of Riesz potential of the right-hand side measure and the oscillation of the boundary data, where the boundary data is given on Q₂_R ∩ {(x¹, x', t) є Rⁿ⁺¹: X¹ = 0}.

Original language	English
Pages (from-to)	61-99
Number of pages	39
Journal	Communications in Analysis and Mechanics
Volume	17
Issue number	1
DOIs	https://doi.org/10.3934/cam.2025004
State	Published - 2025

Keywords

Measurable nonlinearities
Nonlinear parabolic equations
Riesz potentials

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abstract = "We obtain a boundary pointwise gradient estimate on a parabolic half cube Q2R ∩\{(x1, x', t) є Rn+1: X1 > 0\} for nonlinear parabolic equations with measurable nonlinearities, which are only assumed to be measurable in x1-variable. The estimates are obtained in terms of Riesz potential of the right-hand side measure and the oscillation of the boundary data, where the boundary data is given on Q2R ∩ \{(x1, x', t) є Rn+1: X1 = 0\}.",

keywords = "Measurable nonlinearities, Nonlinear parabolic equations, Riesz potentials",

author = "Lee, \{Ho Sik\} and Youchan Kim",

year = "2025",

doi = "10.3934/cam.2025004",

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AU - Kim, Youchan

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AB - We obtain a boundary pointwise gradient estimate on a parabolic half cube Q2R ∩{(x1, x', t) є Rn+1: X1 > 0} for nonlinear parabolic equations with measurable nonlinearities, which are only assumed to be measurable in x1-variable. The estimates are obtained in terms of Riesz potential of the right-hand side measure and the oscillation of the boundary data, where the boundary data is given on Q2R ∩ {(x1, x', t) є Rn+1: X1 = 0}.

KW - Measurable nonlinearities

KW - Nonlinear parabolic equations

KW - Riesz potentials

UR - https://www.scopus.com/pages/publications/85218772395

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DO - 10.3934/cam.2025004

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SP - 61

EP - 99

JO - Communications in Analysis and Mechanics

JF - Communications in Analysis and Mechanics

IS - 1

ER -

Boundary riesz potential estimates for parabolic equations with measurable nonlinearities

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Keywords

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