18 citations · 30 across the 8 of their papers we have counts for
9 papers
-surfaces with free boundaries
Hayk Aleksanyan, Aram L. Karakhanyan
A well-known question in classical differential geometry and geometric analysis asks for a description of possible boundaries of -surfaces, which are smooth, compact hypersurfac…
Perturbed divisible sandpiles and quadrature surfaces
Hayk Aleksanyan, Henrik Shahgholian
The main purpose of the present paper is to establish a link between quadrature surfaces (potential theoretic concept) and sandpile dynamics (Laplacian growth models). For this aim…
Discrete Balayage and Boundary Sandpile
Hayk Aleksanyan, Henrik Shahgholian
We introduce a new lattice growth model, which we call boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on ($d\geq…
Slow convergence in periodic homogenization problems for divergence type elliptic operators
Hayk Aleksanyan
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. Th…
-estimates for singular oscillatory integral operators
Hayk Aleksanyan, Henrik Shahgholian, Per Sjölin
In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of type for the operat…
Regularity of boundary data in periodic homogenization of elliptic systems in layered media
Hayk Aleksanyan
In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the…
Applications of Fourier analysis in homogenization of Dirichlet problem III: Polygonal Domains
Hayk Aleksanyan, Henrik Shahgholian, Per Sjölin
In this paper we prove convergence results for the homogenization of the Dirichlet problem with rapidly oscillating boundary data in convex polygonal domains. Our analysis is based…
Applications of Fourier analysis in homogenization of Dirichlet problem II. estimates
Hayk Aleksanyan, Per Sjölin, Henrik Shahgholian
Let $u_\e$ be a solution to the system $$ \mathrm{div}(A_\e(x) \nabla u_{\e}(x))=0 \text{\ in} D, \qquad u_{\e}(x)=g(x,x/\e) \text{\ on}\partial D, $$ where ($d \…
Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise Estimates
Hayk Aleksanyan, Henrik Shahgholian, Per Sjölin
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on a…