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…