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The mixed problem for the Lam'e system in two dimensions | | Katharine A. Ott
; Russell M. Brown
; | | Date: |
15 Nov 2012 | | Abstract: | We consider the mixed problem for $L$ the Lam’e system of elasticity in a
bounded Lipschitz domain $ Omegasubset
eals ^2$. We suppose that the
boundary is written as the union of two disjoint sets, $partialOmega =Dcup
N$. We take traction data from the space $L^p(N)$ and Dirichlet data from a
Sobolev space $ W^{1,p}(D)$ and look for a solution $u$ of $Lu =0$ with the
given boundary conditions. We give a scale invariant condition on $D$ and find
an exponent $ p_0 >1$ so that for $1<p<p_0$, we have a unique solution of this
boundary value problem with the non-tangential maximal function of the gradient
of the solution in $L^ p(partialOmega)$. We also establish the existence of a
unique solution when the data is taken from Hardy spaces and Hardy-Sobolev
spaces with $ p$ in $(p_1,1]$ for some $p_1 <1$. | | Source: | arXiv, 1211.3655 | | Services: | Forum | Review | PDF | Favorites | |
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