Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy [article]

Peter Lewintan and Stefan Müller and Patrizio Neff
2020 arXiv   pre-print
Let Ω⊂ℝ^3 be an open and bounded set with Lipschitz boundary and outward unit normal ν. For 11 if p = 3/2. Specifically, there exists a constant c=c(p,Ω,r)>0 such that the inequality P _L^p≤ c (sym P _L^p + devsymCurl P _L^r) holds for all tensor fields P∈ W^1, p, r_0(devsymCurl). Here, dev X := X -1/3tr(X) 1 denotes the deviatoric (trace-free) part of a 3 × 3 matrix X and the boundary condition is understood in a suitable weak sense.
arXiv:2011.10573v2 fatcat:aihvzf5nk5dznitghpj6c7w7wi