Bloch principle for elliptic differential operators with periodic coefficients

DOI10.1134/S1061920816020114zbMath1351.35026MaRDI QIDQ327096

S. E. Pastukhova, Vasilii V. Jikov

Publication date: 13 October 2016

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

1-periodic coefficientsBloch principleelliptic equations of divergent typeSobolev spaces with measure

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Operator-norm convergence estimates for elliptic homogenization problems on periodic singular structures ⋮ Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation ⋮ Large-time asymptotics of fundamental solutions for diffusion equations in periodic media and its application to averaging-theory estimates ⋮ On the convergence of Bloch eigenfunctions in homogenization problems ⋮ On the behavior of the solution of the Cauchy problem for an inhomogeneous hyperbolic equation with periodic coefficients ⋮ Behavior of the solution of the Cauchy problem for a hyperbolic equation with periodic coefficients ⋮ Operator-norm homogenisation estimates for the system of Maxwell equations on periodic singular structures

Cites Work

• Approximations of the exponential of an operator with periodic coefficients
• Weighted Sobolev spaces
• Connectedness and homogenization. Examples of fractal conductivity
• On an extension of the method of two-scale convergence and its applications
• Homogenization of elasticity problems on singular structures
• HANS BETHE'S CONTRIBUTIONS TO SOLID-STATE PHYSICS
• Floquet theory for partial differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item