The mixed problem for the Lamé system in a class of Lipschitz domains

DOI10.1016/j.jde.2009.01.008zbMath1165.35008OpenAlexW2035422931MaRDI QIDQ1014712

Russell M. Brown, Irina Mitrea

Publication date: 29 April 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.01.008

zbMATH Keywords

well-posednessmixed boundary value problemsLipschitz domainsLamé systemlayer potentials

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Fredholm integral equations (45B05)

Related Items

On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators, Mixed problems in a Lipschitz domain for strongly elliptic second-order systems, Boundary value problems for the Lamé-Navier system in fractal domains, The mixed problem for the Lamé system in two dimensions, On singularities of solution of the elasticity system in a bounded domain with angular corner points, Layer potentials for the harmonic mixed problem in the plane, The mixed problem for the Laplacian in Lipschitz domains, Mixed boundary value problems for the Stokes system, The \(p\)-ellipticity condition for second order elliptic systems and applications to the Lamé and homogenization problems, Integral representation formulas related to the Lamé-Navier system, Extending Sobolev functions with partially vanishing traces from locally \(({\epsilon},{\delta})\)-domains and applications to mixed boundary problems, On the role of poroelasticity for modeling of stress fields in geothermal reservoirs, Boundary value problems of Robin type for the Brinkman and Darcy-Forchheimer-Brinkman systems in Lipschitz domains, Integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions, Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain, Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition, The 𝐿^{𝑝} Dirichlet boundary problem for second order elliptic Systems with rough coefficients, The L^p Dirichlet and regularity problems for second order elliptic systems with application to the Lamé system, On a generalized Lamé-Navier system in \(\mathbb{R}^3\)

Cites Work

• New bounds for solutions of second order elliptic partial differential equations
• Layer potentials and boundary value problems for elliptic systems in Lipschitz domains
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• Singularités en élasticité. (Singularities in elasticity)
• The mixed problem in \(L^{p}\) for some two-dimensional Lipschitz domains
• Spectral theory and complex interpolation
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Potential techniques for boundary value problems on \(C^1\)-domains
• The Neumann problem on Lipschitz domains in Hardy spaces of order less than one
• On the traction problem for the Lamé system on curvilinear polygons
• Counterexamples to the well-posedness of 𝐿^{𝑝} transmission boundary value problems for the Laplacian
• The linear constraints in Poincaré and Korn type inequalities
• The mixed problem for laplace's equation in a class of lipschitz domains
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item