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Optimal estimates for elliptic equations and systems from composite material
澳门新葡8455最新网站:2017年06月05日 09:39 点击数:

报告人:李海刚

报告地点:澳门新葡8455最新网站二楼会议室

报告澳门新葡8455最新网站:2017年06月07日星期三15:00-16:00

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报告摘要:

We study a class of second-order elliptic equations and systems of divergence form, with discontinuous coefficients and data, which models the conductivity problem in composite materials. For the scalar case, we establish optimal gradient estimates by showing the explicit dependence of the elliptic coefficients and the distance between interfacial boundaries of inclusions. The novelty of these estimates is that they unify the known results in the literature and answer open problem (b) proposed by Li-Vogelius (2000) for the isotropic conductivity problem. We also obtain more interesting higher-order derivative estimates, which answers open problem (c) of Li-Vogelius (2000). This is based on a joint work with Hongjie Dong.

主讲人概况:

李海刚,北京师范大学副教授,博士生导师,霍英东基金获得者。国家自然基金面上项目主持人,国家自然基金重点项目主要成员。主要研究来自材料力学和几何学中的线性和非线性偏微分方程理论。在复合材料中Lame方程组解的梯度估计(Babuska问题)和Monge-Ampere方程、Hessian方程的外Dirichlet问题等方面做出一系列深刻的原创性成果,在《Adv.Math.》、《Arch. Ration. Mech. Anal.》、《Trans. Amer. Math. Soc.》、《Calc. Var. Partial Differential Equations》、《SIAM J.Math. Anal.》、《J. Differential Equations》等SCI国际主流数学杂志上发表科研论文20余篇。

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