Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

The Anh Bui; Xuan Thinh Duong

doi:10.1007/s00526-017-1273-y

Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

The Anh Bui, Xuan Thinh Duong^*

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.

Original language	English
Article number	177
Pages (from-to)	1-27
Number of pages	27
Journal	Calculus of Variations and Partial Differential Equations
Volume	56
Issue number	6
DOIs	https://doi.org/10.1007/s00526-017-1273-y
Publication status	Published - 1 Dec 2017

Keywords

35K61
35R05
46E30

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10.1007/s00526-017-1273-y

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abstract = "The main aim of this paper is to prove the Calder{\'o}n–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.",

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AU - Bui, The Anh

AU - Duong, Xuan Thinh

PY - 2017/12/1

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N2 - The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.

AB - The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.

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KW - 35R05

KW - 46E30

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M3 - Article

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ER -

Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

Abstract

Keywords

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