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9 papers · 1 filter
Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions
Ellen ShiTing Bao, YanYan Li, Biao Yin
In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in . For these two extreme c…
A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
Marta Lewicka
We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness and around the mid-surface of arbitrary geometry, converge as $h\to…
Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space
I. Gyongy, N. Krylov
We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order parabolic and elliptic equat…
The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
Marta Lewicka, Maria Giovanna Mora, Mohammad Reza Pakzad
Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under t…
Second-order elliptic equations with variably partially VMO coefficients
N. V. Krylov
The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal direc…
Diffusive stability of oscillations in reaction-diffusion systems
Thierry Gallay, Arnd Scheel
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the ne…