129 citations · 136 across the 5 of their papers we have counts for
9 papers
-calculus for the Dirichlet Laplacian on conical domains
Petru A. Cioica-Licht, Emiel Lorist, P. Tobias Werner
We establish boundedness of the -calculus for the Dirichlet Laplacian on conical domains in and corresponding wedges on -spaces with mixed weights. Th…
Sobolev spaces with mixed weights and the Poisson equation on angular domains
Petru A. Cioica-Licht, Cornelia Schneider, Markus Weimar
We introduce and analyse a class of weighted Sobolev spaces with mixed weights on angular domains. The weights are based on both the distance to the boundary and the distance to th…
Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations
Petru A. Cioica-Licht, Martin Hutzenthaler, P. Tobias Werner
We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, whi…
An -theory for the stochastic heat equation on angular domains in with mixed weights
Petru A. Cioica-Licht
We establish a refined -estimate () for the stochastic heat equation on angular domains in with mixed weights based on both, the distance to the bounda…
On the limit regularity in Sobolev and Besov scales related to approximation theory
Petru A. Cioica-Licht, Markus Weimar
We study the interrelation between the limit -Sobolev regularity of (classes of) functions on bounded Lipschitz domains , …
Inner products for Convex Bodies
David Bryant, Petru Cioica-Licht, Lisa Orloff Clark +1
We define a set inner product to be a function on pairs of convex bodies which is symmetric, Minkowski linear in each dimension, positive definite, and satisfies the natural analog…