7 citations · 10 across the 13 of their papers we have counts for
16 papers
Schauder and Riesz Bases for Higher-Dimensional Lebesgue Spaces Inspired by ReLU Neural Networks
Julian Billner, Cornelia Schneider
Motivated by the role of piecewise linear functions in ReLU neural networks, we study systems of dilated functions in the Lebesgue spaces , . For a se…
Fractional gradients and nonlocal PDEs in variable exponent spaces
Susana Moura, Cornelia Schneider
We develop a theory of distributional Riesz fractional gradients in variable exponent Lebesgue spaces and introduce the associated nonlocal Sobolev spaces. Moreover, Sobolev, Hardy…
A multivariate Riesz basis of ReLU neural networks
Cornelia Schneider, Jan Vybíral
We consider the trigonometric-like system of piecewise linear functions introduced recently by Daubechies, DeVore, Foucart, Hanin, and Petrova. We provide an alternative proof that…
Anisotropic Besov regularity of parabolic PDEs
Stephan Dahlke, Cornelia Schneider
This paper is concerned with the regularity of solutions to parabolic evolution equations. Special attention is paid to the smoothness in the specific anisotropic scale $\ B^{r\mat…
Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type
Stephan Dahlke, Cornelia Schneider
This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we…
Besov regularity of non-linear parabolic PDEs on non-convex polyhedral domains
Stephan Dahlke, Markus Hansen, Cornelia Schneider
This paper is concerned with the regularity of solutions to parabolic evolution equations. We consider semilinear problems on non-convex domains. Special attention is paid to the s…
Approximation classes for adaptive time-stepping finite element methods
Marcelo Actis, Pedro Morin, Cornelia Schneider
We study approximation classes for adaptive time-stepping finite element methods for time-dependent Partial Differential Equations (PDE). We measure the approximation error in $L_2…
Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values
Cornelia Schneider, Flóra Orsolya Szemenyei
We study the regularity of solutions of the Poisson equation with Dirichlet, Neumann and mixed boundary values in polyhedral cones in the specific scale $\…
An extension operator for Sobolev spaces with mixed weights
Markus Hansen, Cornelia Schneider, Flóra Orsolya Szemenyei
We provide an extension operator for weighted Sobolev spaces on bounded polyhedral cones involving a mixture of weights, which measure the distance to the vertex and the edges…
Growth envelopes of some variable and mixed function spaces
Dorothee D. Haroske, Cornelia Schneider, Kristóf Szarvas
We study unboundedness properties of functions belonging Lebesgue and Lorentz spaces with variable and mixed norms using growth envelopes. Our results extend the ones for the corre…
Properties of Kondratiev spaces
Stephan Dahlke, Markus Hansen, Cornelia Schneider +1
In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compa…
Besov regularity of parabolic and hyperbolic PDEs
Stephan Dahlke, Cornelia Schneider
This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in the specific sc…
Symmetries on manifolds: Generalizations of the Radial Lemma of Strauss
Nadine Große, Cornelia Schneider
For a compact subgroup of the group of isometries acting on a Riemannian manifold we investigate subspaces of Besov and Triebel-Lizorkin type which are invariant with respe…
Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces
Cornelia Schneider, Nadine Große
We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depe…
Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces
Cornelia Schneider, Jan Vybíral
We provide non-smooth atomic decompositions for Besov spaces $\Bd(\rn)$, , , defined via differences. The results are used to compute the trace of Besov spac…
Homogeneity property of Besov and Triebel-Lizorkin spaces
Cornelia Schneider, Jan Vybíral
We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces…