W1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains

The Anh Bui; Xuan Truong Le

doi:10.1142/S0219199716500462

W^1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains

The Anh Bui, Xuan Truong Le^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper, we prove the global gradient estimates on the generalized Lebesgue spaces for weak solutions to elliptic quasilinear obstacle problems. It is worth noticing that the coefficients related to the obstacle problems are merely measurable with small BMO norms and the underlying domain does not satisfy any smoothness conditions.

Original language	English
Article number	1650046
Pages (from-to)	1-19
Number of pages	19
Journal	Communications in Contemporary Mathematics
Volume	19
Issue number	6
DOIs	https://doi.org/10.1142/S0219199716500462
Publication status	Published - Dec 2017

Keywords

Nonlinear elliptic problem
irregular obstacle
Reifenberg flat domain
generalized Lebesgue space

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10.1142/S0219199716500462

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title = "W1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains",

abstract = "In this paper, we prove the global gradient estimates on the generalized Lebesgue spaces for weak solutions to elliptic quasilinear obstacle problems. It is worth noticing that the coefficients related to the obstacle problems are merely measurable with small BMO norms and the underlying domain does not satisfy any smoothness conditions.",

keywords = "Nonlinear elliptic problem, irregular obstacle, Reifenberg flat domain, generalized Lebesgue space",

author = "Bui, {The Anh} and Le, {Xuan Truong}",

year = "2017",

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T1 - W1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains

AU - Bui, The Anh

AU - Le, Xuan Truong

PY - 2017/12

Y1 - 2017/12

N2 - In this paper, we prove the global gradient estimates on the generalized Lebesgue spaces for weak solutions to elliptic quasilinear obstacle problems. It is worth noticing that the coefficients related to the obstacle problems are merely measurable with small BMO norms and the underlying domain does not satisfy any smoothness conditions.

AB - In this paper, we prove the global gradient estimates on the generalized Lebesgue spaces for weak solutions to elliptic quasilinear obstacle problems. It is worth noticing that the coefficients related to the obstacle problems are merely measurable with small BMO norms and the underlying domain does not satisfy any smoothness conditions.

KW - Nonlinear elliptic problem

KW - irregular obstacle

KW - Reifenberg flat domain

KW - generalized Lebesgue space

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

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DO - 10.1142/S0219199716500462

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M1 - 1650046

ER -

W^1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains

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