Optimal elliptic Sobolev regularity near three-dimensional multi-material Neumann vertices

DOI10.1007/s10688-014-0062-zzbMath1315.35077OpenAlexW2142247345MaRDI QIDQ2258221

Joachim Rehberg, Hans-Christoph Kaiser, W. Höppner, Günter M. Ziegler, Robert Haller-Dintelmann

Publication date: 3 March 2015

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-014-0062-z

zbMATH Keywords

mixed Dirichlet-Neumann boundary conditionsoptimal Sobolev regularityanisotropic ellipticity in three dimensionselliptic div-grad operatorpiecewise linear 3D flatteningtransmission at material interfaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with biology, chemistry and other natural sciences (35Q92)

Related Items (4)

Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 1: Existence of Optimal Solutions ⋮ The full Keller–Segel model is well-posed on nonsmooth domains ⋮ Optimal Sobolev Regularity for Linear Second-Order Divergence Elliptic Operators Occurring in Real-World Problems ⋮ The square root problem for second-order, divergence form operators with mixed boundary conditions on \(L^p\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal elliptic regularity at the crossing of a material interface and a Neumann boundary edge
• Maximal parabolic regularity for divergence operators including mixed boundary conditions
• On the regularity of weak solutions of quasi-linear elliptic transmission problems on polyhedral domains
• Singularities of solutions of the Neumann problem at a conical point
• Neumann and mixed problems on curvilinear polyhedra
• Regularity results for elliptic equations in Lipschitz domains
• Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients
• Smoothness of linear laminates
• Solutions for quasilinear nonsmooth evolution systems in \(L^p\)
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Elliptic model problems including mixed boundary conditions and material heterogeneities
• Neumann problems and isocapacitary inequalities
• Optimal regularity for elliptic transmission problems including \(C^1\) interfaces
• Optimal Control for the Thermistor Problem
• Singularities of Maxwell interface problems
• Elements of Lipschitz topology
• General interface problems—I
• Weighted Lp estimates of solutions to boundary value problems for second order elliptic systems in polyhedral domains
• The Inhomogeneous Neumann Problem in Lipschitz Domains
• W^1,q REGULARITY RESULTS FOR ELLIPTIC TRANSMISSION PROBLEMS ON HETEROGENEOUS POLYHEDRA
• Regularity results for Laplace interface problems in two dimensions

This page was built for publication: Optimal elliptic Sobolev regularity near three-dimensional multi-material Neumann vertices