ترغب بنشر مسار تعليمي؟ اضغط هنا

Quantitative strong unique continuation for the Lame system with less regular coefficients

81   0   0.0 ( 0 )
 نشر من قبل Jenn-Nan Wang
 تاريخ النشر 2010
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper we prove a quantitative form of the strong unique continuation property for the Lame system when the Lame coefficients $mu$ is Lipschitz and $lambda$ is essentially bounded in dimension $nge 2$. This result is an improvement of our earlier result cite{lin5} in which both $mu$ and $lambda$ were assumed to be Lipschitz.

قيم البحث

اقرأ أيضاً

We establish upper bounds on the blow-up rate of the gradients of solutions of the Lam{e} system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero.
In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space RN. This kind of observability indicates that the total ene rgy of solutions can be controlled by the energy localized in a measurable subset, which is equidistributed over the whole space. The proof of our results is based on an interesting reduction method [18, 22], as well as the propagation of smallness for the gradient of solutions to elliptic equations [24].
In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a domain, we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain. Using the corresponding Riemann function, we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives. Further, we construct several examples showing the possibility of further reducing the additional information of the other component. This result possesses remarkable significance in both theoretical and practical aspects because the required data is almost halved for the unique determination of the whole solution.
For two neighbouring stiff inclusions, the stress, which is the gradient of a solution to the Lam{e} system of linear elasticity, may exhibit singular behavior as the distance between these two inclusions becomes arbitrarily small. In this paper, a f amily of stress concentration factors, which determine whether the stress will blow up or not, are accurately constructed in the presence of the generalized $m$-convex inclusions in all dimensions. We then use these stress concentration factors to establish the optimal upper and lower bounds on the stress blow-up rates in any dimension and meanwhile give a precise asymptotic expression of the stress concentration for interfacial boundaries of inclusions with different principal curvatures in dimension three. Finally, the corresponding results for the perfect conductivity problem are also presented.
In these notes we prove log-type stability for the Calderon problem with conductivities in $ C^{1,varepsilon}(bar{Omega}) $. We follow the lines of a recent work by Haberman and Tataru in which they prove uniqueness for $ C^1(bar{Omega}) $.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا