Differentiability of solutions to second-order elliptic equations via dynamical systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Maz'ya, Vladimir^2,3  McOwen, Robert¹ 

[1] Brigham & Womens Hosp, Boston, MA 02115 USA

[2] Linkoping Univ, S-58183 Linkoping, Sweden

[3] Univ Liverpool, Liverpool L69 3BX, Merseyside, England

关键词: Differentiability;    Weak solution;    Elliptic equation;    Divergence form;    Modulus of continuity;    Dini condition;    Square-Dini condition;    Dynamical system;    Asymptotically constant;    Uniformly stable;   

DOI  :  10.1016/j.jde.2010.06.023

来源: Elsevier

【 摘 要 】

For a second-order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of continuity satisfying the square-Dini condition, and obtain additional conditions that examples show are sharp. Our results extend those of previous authors who assume the modulus of continuity satisfies the Dini condition. Our method involves the study of asymptotic properties of solutions to a dynamical system that is derived from the coefficients of the elliptic equation. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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