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Date Published: 30/06/2022
Online Published: 30/06/2022
Abstract Views: 188
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DOI: https://doi.org/10.54607/hcmue.js.19.7.3435(2022)
Issue
Vol. 19 No. 6 (2022)
Section
Natural Sciences and Technology
How to Cite
Trần , H. L. (2022). A GLOBAL AND POINTWISE GRADIENT ESTIMATE FOR SOLUTIONS TO DOUBLE-PHASE PROBLEMS IN ORLICZ SPACES. HCMUE Journal of Science, 19(6), 856. https://doi.org/10.54607/hcmue.js.19.7.3435(2022)

A GLOBAL AND POINTWISE GRADIENT ESTIMATE FOR SOLUTIONS TO DOUBLE-PHASE PROBLEMS IN ORLICZ SPACES

Hương Lan Trần 1,
1 Đại học Sư phạm kỹ thuật TP HCM 01 Võ Văn Ngân, phường Linh Chiểu thành phố Thủ Đức thành phố Hồ Chí Minh

Main Article Content

Abstract

 

 

The aim of this paper is twofold. Firstly, we give a global estimate of the Calderón-Zygmund type for solutions to double-phase problems in Orlicz spaces via maximal fractional functions. In this study, we employ the approach based on a generalized good-  technique developed by Tran and Nguyen (2019), where regularity results are preserved under the fractional maximal operator. This operator is notable for its role in evaluating the oscillation of functions, and there is a close relation between this operator and the Riesz potential. Secondly, we present a pointwise estimate of the Riesz potential as a consequence of the first result.

 

Keywords

Double-phase problems, Orlicz spaces, gradient estimates, Riesz potential, fractional maximal functions

Article Details

References

Byun, S. S., & Oh, J. (2017). Global gradient estimates for non-uniformly elliptic equations.
Calc. Var. Partial Differ. Equ., 56(2).
Colombo, M., & Mingione, G. (2016). Calderón-Zygmund estimates and non-uniformly elliptic operators. J. Funct. Anal., 270(4), 1416-1478.
Filippis, C. De, & Mingione, G. (2019). A borderline case of Calderón-Zygmund estimates for non-uniformly elliptic problems. St. Petersburg Math. J., 31(3), 82-115.
Harjulehto, P., & Hasto, P. (2019). Generalized Orlicz spaces. Lecture notes in Mathematics, Springer International Publishing.
Nguyen, T. N., & Tran, M. P. (2021). Level-set inequalities on fractional maximal distribution functions and applications to regularity theory. Journal of functional analysis, 280, 108797.
Nguyen, T. N., & Tran, M. P. (2021). Lorentz improving estimates for the -Laplace equations with mixed data. Nonlinear Analysis 200, 111960.
Tran, M. P., & Nguyen, T. N. (2019). Generalized good- techniques and applications to weighted Lorentz regularity for quasilinear elliptic equations. Comptes Rendus Mathematique, 357(8), 664-670.
Tran, M. P., & Nguyen, T. N. (2021). Global Lorentz estimates for non-uniformly nonlinear elliptic equations via fractional maximal operators. Journal of mathematical analysis and applications, 501, 124084