Eigenvalue homogenization for quasilinear elliptic operators in one space dimension
Julian Fernandez Bonder, Juan Pablo Pinasco, Ariel M. Salort
备注：
This paper has been withdraw due to an improvement on the results that will be uploaded as a different article soon. The results in the new article will include also the ones in 1201.1219
In this paper we study the rate of convergence of the eigenvalues of 1-dimensional rapidly oscillating $p-$laplacian type problems and find explicit order of convergence both in $k$ and in $\ve$. Moreover, explicit bounds on the constant entering in the estimate are also obtained.
Homogenization and Shape Differentiation of Quasilinear Elliptic Equations
本文共分为五章。其目的是研究R.半线性椭圆型方程的Aris。第一章主要研究小颗粒区域中拟线性扩散反应问题的均匀化。经典的结果被推广到更一般的形状，特别是新的临界情况。第二章研究半线性椭圆型和抛物型方程的Steiner对称化。第三章讨论光滑和非光滑非线性的形状微分。第四章研究了带位势$-Δu + \nabla u \cdot b + V u$的线性椭圆型方程，其中位势$V$在边界附近“爆炸”。在非光滑情况下，这类方程是形状微分过程的结果。第五章发展了论文的第二部分，并包括2017年访问Brezis教授期间获得的结果。证明了具有Dirichlet边界条件的$-Δ$的特征值基是用$L^2$最优逼近$H_0^1$中函数的唯一基.
Periodic operators over a component domain and homogenization of some class of quasi-linear elliptic problems in two-component domain with interfacial resistance
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