Lp estimates of solutions tomixed boundary value problems for the Stokes system in polyhedral domains

A mixed boundary value problem for the Stokes system in a polyhedral domain is considered. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescr ...

[1]  Juergen Rossmann,et al.  Pointwise estimates for Green's kernel of a mixed boundary value problem to the Stokes system in a polyhedral cone , 2004, math-ph/0412068.

[2]  Zhongwei Shen,et al.  Estimates for the Stokes Operator in Lipschitz Domains , 1995 .

[3]  Vladimir Maz’ya,et al.  Weighted Lp estimates of solutions to boundary value problems for second order elliptic systems in polyhedral domains , 2003 .

[4]  V. Maz'ya,et al.  Estimates for Green ' s matrix of boundary value problems for theStokes system in a polyhedral oneby , 2022 .

[5]  J. Rossmann.  On two classes of weighted Sobolev-Slobodetskiĭ spaces in a dihedral angle , 1992 .

[6]  E. N. Dancer.  ELLIPTIC PROBLEMS IN DOMAINS WITH PIECEWISE SMOOTH BOUNDARIES (de Gruyter Expositions in Mathematics 13) , 1996 .

[7]  R. Kellogg,et al.  A regularity result for the Stokes problem in a convex polygon , 1976 .

[8]  W. Wahl,et al.  Strong Solutions of the Navier–Stokes System in Lipschitz Bounded Domains , 1995 .

[9]  Vladimir Maz'ya,et al.  Point Estimates for Green's Matrix to Boundary Value Problems for Second Order Elliptic Systems in a Polyhedral Cone , 2002 .

[10]  Marius Mitrea,et al.  The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains , 2004 .

[11]  Vladimir Maz’ya,et al.  Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations , 2000 .

[12]  J. Roßmann,et al.  Elliptic Boundary Value Problems in Domains with Point Singularities , 2002 .

[13]  F. Thomasset.  Finite element methods for Navier-Stokes equations , 1980 .

[14]  Carlos E. Kenig,et al.  The Dirichlet problem for the Stokes system on Lipschitz domains , 1988 .

[15]  Anna-Margarete Sändig,et al.  Elliptic Boundary Value Problems in Domains with Edges , 1987 .

[16]  Monique Dauge,et al.  Stationary Stokes and Navier-Stokes systems on two-or three-dimensional domains with corners , 1989 .

[17]  Serge Nicaise,et al.  Regularity of the solutions of elliptic systems in polyhedral domains. , 1997 .

[18]  Zhongwei Shen.  The Lp boundary value problems on Lipschitz domains , 2006 .

[19]  C. Schwab,et al.  On singularities of solutions to the Dirichlet problem of hydrodynamics near the vertex of a cone. , 1994 .

[20]  V. Mazya,et al.  Schauder estimates for solutions to boundary value problems for second order elliptic systems in polyhedral domains , 2004 .

[21]  V. A. Kondrat'ev,et al.  Boundary problems for elliptic equations in domains with conical or angular points , 1967 .

[22]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[23]  Jürgen Rossmann,et al.  Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten , 1988 .

[24]  S. Agmon,et al.  Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I , 1959 .

[25]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[26]  R. Glowinski.  Finite element methods for incompressible viscous flow , 2003 .

[27]  B. Plamenevskii,et al.  Elliptic Problems in Domains with Piecewise Smooth Boundaries , 1994 .

[28]  Liudas Stupelis.  Navier-Stokes Equations in Irregular Domains , 1995 .

[29]  V. Maz'ya,et al.  The first boundary value problem for classical equations of mathematical physics in domains with piecewise-smooth boundaries. I (in Russian) , 1983 .

[30]  M. Dauge.  Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions , 1988 .