Remarks on a paper by Leonetti and Siepe

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Gao Hongya¹  Liu Chao¹  Tian Hong¹ 

[1] Hebei Univ, Coll Math & Comp Sci, Baoding 071002, Peoples R China

关键词: Integrability;    Anisotropic elliptic equation;    Anisotropic obstacle problem;   

DOI  :  10.1016/j.jmaa.2012.12.037

来源: Elsevier

【 摘 要 】

In (2012), Leonetti and Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type {Sigma(n)(i=1) D-i(a(i)(x, Du(x))) = 0, x is an element of Omega, u(x) = theta(x), x is an element of Omega. Under some suitable conditions, they obtained an integrability result, which shows that higher integrability of the boundary datum theta forces solutions u to have higher integrability as well. In the present paper, we consider K-psi,0((pi))-obstacle problems of the nonhomogeneous anisotropic elliptic equations Sigma(n)(i=1) D-i(a(i)(x, Du(x))) = Sigma(n)(i=1) D(i)f(i)(x) under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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