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Date Published: 31/01/2023
Online Published: 31/01/2023
Abstract Views: 264
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DOI: https://doi.org/10.54607/hcmue.js.20.1.3418(2023)
Issue
Vol. 20 No. 1 (2023)
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Articles
How to Cite
Trần , Đ. Đ. P., Nguyễn , H. H., & Trần , P. A. (2023). REGULARITY RESULTS FOR SOLUTIONS TO p-LAPLACE EQUATIONS CONTAINING SCHRÖDINGER TERMS IN LORENTZ SPACES WITH. HCMUE Journal of Science, 20(1), 92. https://doi.org/10.54607/hcmue.js.20.1.3418(2023)

REGULARITY RESULTS FOR SOLUTIONS TO p-LAPLACE EQUATIONS CONTAINING SCHRÖDINGER TERMS IN LORENTZ SPACES WITH

Đại Đình Phong Trần , Hữu Hải Nguyễn , Phước An Trần

Main Article Content

Abstract

The p-Laplace equations containing the Schrödinger terms have been extensively applied in science. Recently, the regularity of the solution to this equation has been studied in different function spaces. This paper present the regularity results for solutions to p-Laplace equations containing the Schrödinger terms in Lorentz spaces with  . The method used is to establish the distribution function inequality on the level sets of quantities related to the gradient of the solution and the given data under the influence of fractional maximal operators. This method has been recently developed and used effectively.

 

 

Keywords

fractional-level maximal operator, gradient estimates, Lorentz space, p-Laplace equation, regularity theory

Article Details

References

Caffarelli, L. A, & Peral, I. (1998). On W1.p estimates for elliptic equations in divergence form. Commun. Pure Appl. Math., 51(1), 1-21.
Calderón, A. P., & Zygmund, A. (1952). On the existence of certain singular integrals. Acta Math. 88, 85-139.
Cruz-Uribe, D., & Neugebauer, C. J. (1995). The structure of the reverse Hölder classes. Transactions of the American Mathematical Society, 347(8), 2941-2960.
Hamburger, C. (1992). Regularity of differential forms minimizing degenerate elliptic functionals, J. Reine Angew. Math. (Crelles J.), 431, 7-64.
Johnson, R., & Neugebauer, C. J. (1991). Change of variable results for - and reverse Hölder - classes. Transactions of the American Mathematical Society, 328(2), 639-666.
Lee, M., & Ok, J. (2020). Interior and boundary W1,p -estimates for elliptic quasilinear equations of Schrödinger type. J. Differ. Equ., 269(5), 4406-4439.
Lee, M., & Ok, J. (2021). Lp regularity for nonlinear elliptic equations with Schrödinger -type lower order terms, preprint, arXiv:2108.13779.
Nguyen, T. N., & Tran, M. P. (2020a). Lorentz improving estimates for the p-Laplace equations with mixed data. Nonlinear Anal., 200, 111960.
Nguyen, T. N., & Tran, M. P (2021a), Level-set inequalities on fractional maximal distribution functions and applications to regularity theory. J. Funct. Anal., 280(1), 108797.
Nguyen, T. N., & Tran, M. P (2021b). Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schrödinger term. Math. Methods Appl. Sci., 44(7), 6101-6116.
Nguyen, T. N., Tran, Q. V., Huynh, P. N., & Tran, M. P. (2022). Weighted distribution approach for a class of nonlinear elliptic equations associated to Schrödinger-type operators, preprint,
17 pages.
Tran, M. P., & Nguyen, T. N. (2019a). Generalized good- techniques and applications to weighted Lorentz regularity for quasilinear elliptic equations. C. R. Acad. Sci. Paris, Ser. I, 357(8),
664-670.
Tran, M. P., & Nguyen, T. N. (2019b). Gradient estimates via Riesz potentials and fractional maximal operators for quasilinear elliptic equations with applications, preprint, arXiv:1907.01434v2.
Tran, M. P., & Nguyen, T. N. (2020). New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data. J. Differ. Equ., 268(4),
1427-1462.
Tran, M. P., & Nguyen, T. N. (2022a). Weighted distribution approach to gradient estimates for quasilinear elliptic double-obstacle problems in Orlicz spaces. J. Math. Anal. Appl., 509(1), 125928.
Tran, M. P., & Nguyen, T. N. (2022b). Global gradient estimates for very singular quasilinear elliptic equations with non-divergence data. Nonlinear Anal., 214, 112613.
Tran, M. P., Nguyen, T. N, & Huynh, P. N. (2021). Calderón-Zygmund-type estimates for singular quasilinear elliptic obstacle problems with measure data, preprint, arXiv:2109.01026v2.
Tran, M. P., Nguyen, T. N., & Nguyen, G. B. (2021). Lorentz gradient estimates for a class of elliptic p-Laplacian equations with a Schrödinger term. J. Math. Anal. Appl., 496(1), 124806.
Tran, M. P., Nguyen, T. N., Pham, L. T. N., & Dang, T. T. T. (2021). Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents, preprint, 14 pages.
Shen, Z. (1995). estimates for Schrödinger operators with certain potentials. Ann. Inst. Fourier, 45(2), 513-546.
Vitali, G. (1908). Sui gruppi di punti e sulle funzioni di variabili reali. Atti R. Accad. Sci. Torino, 43, 229-246.