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Boundary layer tails in periodic homogenization

Grégoire Allaire, Micol Amar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focus on the properties of boundary layers in periodic homogenization in rectangular domains which are either fixed or have an oscillating boundary. Such boundary layers are highly oscillating near the boundary and decay exponentially fast in the interior to a non-zero limit that we call boundary layer tail. The influence of these boundary layer tails on interior error estimates is emphasized. They mainly have two effects (at first order with respect to the period ε): first, they add...

Boundary regularity of flows under perfect slip boundary conditions

Petr Kaplický, Jakub Tichý (2013)

Open Mathematics

We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.

Boundary value problems and duality between Lp Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains.

Kaj Nyström (2006)

Collectanea Mathematica

In this paper we consider general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylindersΩ = {(x0,x,t) ∈ R x Rn-1 x R: x0 > A(x,t)}.We prove solvability of Dirichlet, Neumann as well as regularity type problems with data in Lp and Lp1,1/2 (the parabolic Sobolev space having tangential (spatial) gradients and half a time derivative in Lp) for p ∈ (2 − ε, 2 + ε) assuming...

Currently displaying 141 – 160 of 195