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Asymptotics of energy integrals under small perturbations of the boundary close to angular and conic points. (Russian) Zbl 0668.35027
This paper deals with the deduction and mathematical proof of asymptotic formulas of functionals of energy integral type in connection with boundary problems for elliptic systems of Douglis-Nirenberg \[ {\mathcal L}(x,D_ x)v(x)={\mathcal F}(x),\quad {\mathcal B}(x,D_ x)v(x)={\mathcal G}(x),\quad x\in \Omega \] where \({\mathcal L}\) and \({\mathcal B}\) are \(k\times k\) and \(m\times k\)-matrix differential operators. Here boundary value problems are studied with small perturbations of the boundary close to a conic (angular) point or an isolated point.
Reviewer: J.H.Tian

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B20 Perturbations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs