Partial regularity for elliptic equations

Guji Tian; Xu Jia Wang

doi:10.3934/dcds.2010.28.899

Partial regularity for elliptic equations

Guji Tian^*, Xu Jia Wang

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

In this paper we study partial and anisotropic Schauder estimates for linear and nonlinear elliptic equations. We prove that if the inhomogeneous term f is Hölder continuous in the x_n-direction, then the mixed derivatives u_xxn are Hölder continuous; if f satisfies an anisotropic Hölder continuity condition, then the second derivatives D ²_u satisfy related anisotropic Hölder continuity estimates.

Original language	English
Pages (from-to)	899-913
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems
Volume	28
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2010.28.899
Publication status	Published - Nov 2010

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title = "Partial regularity for elliptic equations",

abstract = "In this paper we study partial and anisotropic Schauder estimates for linear and nonlinear elliptic equations. We prove that if the inhomogeneous term f is H{\"o}lder continuous in the xn-direction, then the mixed derivatives uxxn are H{\"o}lder continuous; if f satisfies an anisotropic H{\"o}lder continuity condition, then the second derivatives D 2u satisfy related anisotropic H{\"o}lder continuity estimates.",

keywords = "Elliptic equation, Partial regularity, Perturbation argument",

author = "Guji Tian and Wang, {Xu Jia}",

year = "2010",

month = nov,

doi = "10.3934/dcds.2010.28.899",

language = "English",

volume = "28",

pages = "899--913",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

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TY - JOUR

T1 - Partial regularity for elliptic equations

AU - Tian, Guji

AU - Wang, Xu Jia

PY - 2010/11

Y1 - 2010/11

N2 - In this paper we study partial and anisotropic Schauder estimates for linear and nonlinear elliptic equations. We prove that if the inhomogeneous term f is Hölder continuous in the xn-direction, then the mixed derivatives uxxn are Hölder continuous; if f satisfies an anisotropic Hölder continuity condition, then the second derivatives D 2u satisfy related anisotropic Hölder continuity estimates.

AB - In this paper we study partial and anisotropic Schauder estimates for linear and nonlinear elliptic equations. We prove that if the inhomogeneous term f is Hölder continuous in the xn-direction, then the mixed derivatives uxxn are Hölder continuous; if f satisfies an anisotropic Hölder continuity condition, then the second derivatives D 2u satisfy related anisotropic Hölder continuity estimates.

KW - Elliptic equation

KW - Partial regularity

KW - Perturbation argument

UR - http://www.scopus.com/inward/record.url?scp=77955313632&partnerID=8YFLogxK

U2 - 10.3934/dcds.2010.28.899

DO - 10.3934/dcds.2010.28.899

M3 - Article

SN - 1078-0947

VL - 28

SP - 899

EP - 913

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 3

ER -

Partial regularity for elliptic equations

Abstract

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