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6 papers · 1 filter
Asymptotic treatment of perforated domains without homogenization
V. Maz'ya, A. Movchan
As a main result of the paper, we construct and justify an asymptotic approximation of Green's function in a domain with many small inclusions. Periodicity of the array of inclusio…
Pointwise estimates for the polyharmonic Green function in general domains
Svitlana Mayboroda, Vladimir Maz'ya
In the present paper we establish sharp pointwise estimates on the polyharmonic Green function and its derivatives in an arbitrary bounded open set.
Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain
Vladimir Maz'ya
It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex -dimensional domain are uniformly Lipschitz. Applications of this result to som…
The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients
Vladimir Maz'ya, Marius Mitrea, Tatyana Shaposhnikova
We study the Dirichlet problem in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order, with bounded, complex-…
Critical Hardy--Sobolev Inequalities
S. Filippas, V. Maz'ya, A. Tertikas
We consider Hardy inequalities in , , with best constant that involve either distance to the boundary or distance to a surface of co-dimension , and we show t…
Boundedness of the Hessian of a biharmonic function in a convex domain
Svitlana Mayboroda, Vladimir Maz'ya
We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dim…