Related papers: Norm convergence for problems with perforation alo…
We consider a boundary value problem for a general second order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric…
We consider a boundary value problem for a general second order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries…
We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric…
For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain $\Omega$ we show that solutions of the corresponding elliptic problem with Robin and thus in…
We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of…
The two scale convergence of the solution to a Robin's type-like problem of a stationary diffusion problem in a periodically perforated domain is investigated. It is shown that the Robin's problem converges to a problem associated to a new…
The paper deals with homogenization problem for nonlinear elliptic and parabolic equations in a periodically perforated domain, a nonlinear Fourier boundary conditions being imposed on the perforation border. Under the assumptions that the…
We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…
We consider a boundary-value problem for the second order elliptic differential operator with rapidly oscillating coefficients in a domain $\Omega_{\epsilon}$ that is $\epsilon-$periodically perforated by small holes. The holes are divided…
Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…
This paper deals with an elliptic problem with a nonlinear lower order term set in an open bounded cylinder of $R^N$, $N\geq 2$, divided into two connected components by an imperfect rough interface. More precisely, we assume that at the…
In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations…
For several different boundary conditions (Dirichlet, Neumann, Robin), we prove norm-resolvent convergence for the operator $-\Delta$ in the perforated domain $\Omega\setminus \bigcup_{ i\in 2\varepsilon\mathbb Z^d }B_{a_\varepsilon}(i),$…
In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance…
We consider Laplace's equation in a periodically perforated domain with Robin boundary conditions on the holes, where the Robin coefficient is scaled proportionally to the inverse total surface area of the performations. We identify a…
In the paper we consider boundary -- value problems with rapidly alternating type of boundary conditions, including problems in domains with perforated boundaries. We present the classification of homogenized (limit) problems depending on…
We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, enter perpendicularly into a support…
Let $n\ge2$ and $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations…
We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the…
We present a new type of approximation of a second-order elliptic operator in a planar domain with a point interaction. It is of a geometric nature, the approximating family consists of operators with the same symbol and regular…