Journal of Hebei University(Natural Science Edition) >

2019 , Vol. 39 >Issue 6: 568 - 572

DOI: https://doi.org/10.3969/j.issn.1000-1565.2019.06.002

Generalization of Holder's inequality and it's applications

  • HUANG Miaomiao ,
  • WANG Fengli ,
  • GAO Hongya
Expand
  • 1.Key Laboratory of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, China; 2.School of Architecture, Shijiazhuang University of Applied Technology, Shijiazhuang 050081, China

Received date: 2019-04-27

  Online published: 2019-11-25

Fold

Abstract

A generalization of the classical Hölders inequality is given, which is applied to the study the boundary value problems of nonlinear divergence type elliptic equation when the boundary value is not zero. The regularity property of the solution is obtained by using Stampacchia lemma and the technique of Sobolev spaces.

Key words： generalization of Hö; lders inequality; boundary value problem; regularity.

Cite this article

HUANG Miaomiao , WANG Fengli , GAO Hongya . Generalization of Holder's inequality and it's applications[J]. Journal of Hebei University(Natural Science Edition), 2019 , 39(6) : 568 -572 . DOI: 10.3969/j.issn.1000-1565.2019.06.002

References

[1] STEIN E, WEISS G. Introduction to Fourier analysis on Euclidean spaces [M]. Priceton:Princeton University Press, 1971.
[2] BOCCARDO L, CROCE G. Elliptic partial differential equations [M]. Berlin: De Gruyter, 2014.
[3] BOCCARDO L, ORSINA L. Leray-Lions operators with logarithmic growth [J]. J Math Anal Appl, 2015, 423: 608-622.
[4] BOCCARDO L, MURAT F, PUEI J P. L∞-estimate for nonlinear elliptic partial differential equations and application to an existence result [J]. SIAMJ Math Anal, 1992, 23(2): 326-333.
[5] CAROZZA M, GAO H, GIOVA R, et al. Local boundedness for minimizers of some polyconvex integrals [J]. J Optim Theory Appl, 2018, 177(3): 699-725.
[6] EVANS L C. Partial differential equations [M]. [s.l.] : American Mathematical Society, 1997.
[7] GAO H, DI Q, MA D. Integrability for solutions to some anisotropic obstacle problems[J]. Manuscripta Math, 2015, 146(3-4): 433-444.
[8] GAO H, LEONETTI F, MACRI M, et al. Regularity for minimizers with positive Jacobian [J]. Applicable Analysis, 2018, 3:1-12.
[9] GILBARG D, TRUDINGER N S. Elliptic partial differential equations of second order [M]. Berlin: Springer-Verlag, 2001.
[10] INNAMORATI A, LEONETTI F. Global integrability for weak solutions to some anisotropic elliptic equations[J]. Nonlinear Anal, 2015, 113: 430-434.
[11] KOVALEVSKY A A. Integrability and boundedness of solutions to some anisotropic problems[J]. J Math Anal Appl, 2015, 432: 820-843.
[12] KOVALEVSKY A A. On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations [J]. Izvestiya Mathematics, 2003, 67(67): 881-894.
[13] LEONETTI F, PETTICCA P V. Summability for solutions to some quasilinear elliptic systems [J]. Ann Mat Pura Appl, 2014, 193: 1671-1682.
[14] STAMPACCHIA G. Equations elliptiques du second order a coefficientes discontinus [J]. Seminaire Jean Leray, 1963-1964, 3:1-37.
[15] GAO H Y, LEONETTI F, WANG L H. Remarks on Stampacchia Lemma [J]. J Math Anal Appl, 2018, 458: 112-122.
Options
Outlines

/

〈 〉