Large-scale regularity of nearly incompressible elasticity in stochastic homogenization

DOI10.1007/s00205-022-01772-6zbMath1491.35096arXiv2004.14568OpenAlexW3023812188MaRDI QIDQ2138648

Shu Gu, Jinping Zhuge

Publication date: 12 May 2022

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.14568

zbMATH Keywords

regularitylinear elasticitystochastic homogenizationCaccioppoli inequalitynearly incompressible materiallarge-scale estimates of displacement and pressureMeyers' estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Homogenization in equilibrium problems of solid mechanics (74Q05) Regularity of solutions of equilibrium problems in solid mechanics (74G40) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Boundary value problems for second-order elliptic systems (35J57)

Related Items

Large-scale regularity for the stationary Navier-Stokes equations over non-Lipschitz boundaries ⋮ Higher-order boundary layers and regularity for Stokes systems over rough boundaries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mesoscopic higher regularity and subadditivity in elliptic homogenization
• Well-posedness of the Stokes-Coriolis system in the half-space over a rough surface
• Boundary estimates in elliptic homogenization
• Convergence rates and \(W^{1,p}\) estimates in homogenization theory of Stokes systems in Lipschitz domains
• Effective boundary condition at a rough surface starting from a slip condition
• Periodic homogenization of elliptic systems
• The Navier wall law at a boundary with random roughness
• Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
• Solutions of the divergence operator on John domains
• Relevance of the slip condition for fluid flows near an irregular boundary
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method
• A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow.
• Quantitative results on the corrector equation in stochastic homogenization
• Improved regularity in bumpy Lipschitz domains
• An analysis of the p-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates
• Scaling limit of the corrector in stochastic homogenization
• Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
• Uniform Lipschitz estimates in bumpy half-spaces
• The additive structure of elliptic homogenization
• Periodic homogenization of Green's functions for Stokes systems
• Degree-independent Sobolev extension on locally uniform domains
• Convergence rates in homogenization of Stokes systems
• Quantitative
• Lipschitz Estimates in Almost-Periodic Homogenization
• Homogenization of Stokes Systems and Uniform Regularity Estimates
• Wall laws for fluid flows at a boundary with random roughness
• An Overlapping Schwarz Algorithm for Almost Incompressible Elasticity
• Compactness methods in the theory of homogenization
• Compactness methods in the theory of homogenization II: Equations in non-divergence form
• Homogenization of elliptic systems with Neumann boundary conditions
• Optimal Boundary Estimates for Stokes Systems in Homogenization Theory
• Quantitative Stochastic Homogenization and Large-Scale Regularity
• Lipschitz regularity for elliptic equations with random coefficients

This page was built for publication: Large-scale regularity of nearly incompressible elasticity in stochastic homogenization