Asymptotics of energy integrals under small perturbations of the boundary close to angular and conic points. (Russian) Zbl 0668.35027

Maz’ya, V. G.; Nazarov, S. A.

Tr. Mosk. Mat. O.-va 50, 79-129 (1987).

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

MSC:

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

Keywords:

asymptotics; energy integrals; small perturbations; systems of Douglis- Nirenberg