Petru A. Cioica-Licht

activity

20062025

most citedStochastic integration in UMD Banach spaces

129 citations · 156 across the 11 of their papers we have counts for

collaborators

11 papers

math.FA2025

$H^{\infty}$ -calculus for the Dirichlet Laplacian on conical domains

Petru A. Cioica-Licht, Emiel Lorist, P. Tobias Werner

We establish boundedness of the $H^{\infty}$ -calculus for the Dirichlet Laplacian on conical domains in $R^{d}$ and corresponding wedges on $L^{p}$ -spaces with mixed weights. Th…

math.AP2024★ 1 cited

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…

math.NA2022★ 5 cited

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…

math.PR2020★ 1 cited

An $L_{p}$ -theory for the stochastic heat equation on angular domains in $R^{2}$ with mixed weights

Petru A. Cioica-Licht

We establish a refined $L_{p}$ -estimate ( $p \geq 2$ ) for the stochastic heat equation on angular domains in $R^{2}$ with mixed weights based on both, the distance to the bounda…

math.FA2019

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 $L_{p} (Ω)$ -Sobolev regularity $s_{p}$ of (classes of) functions on bounded Lipschitz domains $Ω \subseteq R^{d}$ , $d \geq 2$ …

math.MG2018★ 1 cited

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…

math.PR2018★ 15 cited

On the regularity of the stochastic heat equation on polygonal domains in $R^{2}$

Petru A. Cioica-Licht, Kyeong-Hun Kim, Kijung Lee

We establish existence, uniqueness and higher order weighted $L_{p}$ -Sobolev regularity for the stochastic heat equation with zero Dirichlet boundary condition on angular domains and…

math.PR2018

Stochastic integration in quasi-Banach spaces

Petru A. Cioica-Licht, Sonja G. Cox, Mark C. Veraar

In this paper we develop a stochastic integration theory for processes with values in a quasi-Banach space. The integrator is a cylindrical Brownian motion. The main results give s…

math.AP2016

Besov Regularity for the Stationary Navier-Stokes Equation on Bounded Lipschitz Domains

Frank Eckhardt, Petru A. Cioica-Licht, Stephan Dahlke

We use the scale $B_{τ}^{s} (L_{τ} (Ω))$ , $1/ τ = s / d + 1/2$ , $s > 0$ , to study the regularity of the stationary Stokes equation on bounded Lipschitz domains $Ω \subset R^{d}$ , $d \geq 3$ , wi…

math.PR2016★ 4 cited

An $L_{p}$ -estimate for the stochastic heat equation on an angular domain in $R^{2}$

Petru A. Cioica-Licht, Kyeong-Hun Kim, Kijung Lee +1

We prove a weighted $L_{p}$ -estimate for the stochastic convolution associated to the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain $\mat…

math.PR2006★ 129 cited

Stochastic integration in UMD Banach spaces

J. M. A. M. van Neerven, M. C. Veraar, L. Weis

In this paper we construct a theory of stochastic integration of processes with values in $L (H, E)$ , where $H$ is a separable Hilbert space and $E$ is a UMD Banach space (…