2017/05/21 by T. A. Suslina, Suslina, Tatiana · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems #Primary 35B27 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1705.08295
openalex publication_date 2017/05/21 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Let \O\⊂\ℝd be a bounded domain of class C2p.\nIn L2(\O;\ℂn), we study a selfadjoint strongly elliptic\noperator AN,\ε of order 2p given by the expression b( mathbf\nD)^* g( mathbf x/\ε) b( mathbf D), \ε >0, with the\nNeumann boundary conditions. Here g( mathbf x) is a bounded and positive\ndefinite (m\× m)-matrix-valued function in mathbb Rd, periodic with\nrespect to some lattice; b( mathbf D)=\∑|\α|=p b_\α mathbf\nD^\α is a differential operator of order p with constant coefficients;\nb_\α are constant (m\× n)-matrices. It is assumed that m geqslant\nn and that the symbol b( boldsymbol \ξ) has maximal rank for any 0 \≠\n boldsymbol \ξ\∈ mathbb Cd. We find approximations for the resolvent\n\(AN,\ε-\ζ I \)-1 in the\nL2(\O;\ℂn)-operator norm and in the norm of operators\nacting from L2(\O;\ℂn) to the Sobolev space\nHp(\O;\ℂn), with error estimates depending on\n\ε and \ζ.\n