We prove a regularity result for the anisotropic linear elasticity equation P u:=\rm div\left
(\boldmath C ⋅ ∇ u\right)= f, with mixed (displacement and traction) boundary conditions on …

We analyze the complexity of the sparse-grid interpolation and sparse-grid quadrature of
countably-parametric functions which take values in separable Banach spaces with …

We consider the Dirichlet problem for an elliptic equation with a singularity. The singularity of
the solution to the problem is caused by the presence of a re-entrant corner at the boundary …

The Green function of the Poisson equation in two dimensions is not contained in the
Sobolev space H^1(Ω) such that finite element error estimates for the discretization of a …

Deep neural networks (DNNs) for numerical solutions to partial differential equations (PDEs)
have exhibited their remarkable merits of meshless methods, dimensionless features, and …

Let µ∈ Z+ be arbitrary. We prove a well-posedness result for mixed boundary
value/interface problems of second-order, positive, strongly elliptic operators in weighted …

We study families of strongly elliptic, second order differential operators with singular
coefficients on domains with conical points. We obtain uniform estimates on their inverses …

We establish dimension-independent expression rates by deep ReLU networks for certain
countably parametric maps, so-called (b, ε, 𝒳)-holomorphic functions. These are mappings …

This paper is concerned with the discretization of linear elliptic partial differential equations
with Neumann boundary condition in polygonal domains. The focus is on the derivation of …

For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous
elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and for …