Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks
In this work, we explore the numerical solution of geometric shape optimization problems
using neural network-based approaches. This involves minimizing a numerical criterion that …
using neural network-based approaches. This involves minimizing a numerical criterion that …
Boundary value problems on non-Lipschitz uniform domains: stability, compactness and the existence of optimal shapes
M Hinz, A Rozanova-Pierrat, A Teplyaev - Asymptotic Analysis, 2023 - content.iospress.com
We study boundary value problems for bounded uniform domains in R n, n⩾ 2, with non-
Lipschitz, and possibly fractal, boundaries. We prove Poincaré inequalities with uniform …
Lipschitz, and possibly fractal, boundaries. We prove Poincaré inequalities with uniform …
Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks
In this work, we explore the numerical solution of geometric shape optimization problems
using neural network-based approaches. This involves minimizing a numerical criterion that …
using neural network-based approaches. This involves minimizing a numerical criterion that …
The Robin mean value equation II: asymptotic Hölder regularity
We show that solutions to the Robin mean value equations (RMV), introduced in Lewicka
and Peres, converge uniformly in the limit of the vanishing radius of averaging, to the unique …
and Peres, converge uniformly in the limit of the vanishing radius of averaging, to the unique …
The Robin mean value equation I: A random walk approach to the third boundary value problem
We study the family of integral equations, called the Robin mean value equations (RMV),
that are local averaged approximations to the Robin-Laplace boundary value problem (RL) …
that are local averaged approximations to the Robin-Laplace boundary value problem (RL) …
Stability results for the Robin-Laplacian on nonsmooth domains
D Bucur, A Giacomini, P Trebeschi - SIAM Journal on Mathematical Analysis, 2022 - SIAM
We formulate a generalization of the Laplace equation under Robin boundary conditions on
a large class of possibly nonsmooth domains by dealing with the trace term appearing in the …
a large class of possibly nonsmooth domains by dealing with the trace term appearing in the …
Non-concavity of the Robin ground state
On a convex bounded Euclidean domain, the ground state for the Laplacian with Neumann
boundary conditions is a constant, while the Dirichlet ground state is log-concave. The …
boundary conditions is a constant, while the Dirichlet ground state is log-concave. The …
Non-concavity of Robin eigenfunctions
On a convex bounded Euclidean domain, the ground state for the Laplacian with Neumann
boundary conditions is a constant, while the Dirichlet ground state is log-concave. The …
boundary conditions is a constant, while the Dirichlet ground state is log-concave. The …
Learning-based geometric shape optimization of the Dirichlet energy
In this work, we explore the numerical solution of geometric shape optimization problems
using neural network-based approaches. This involves minimizing a numerical criterion that …
using neural network-based approaches. This involves minimizing a numerical criterion that …
Shape optimization problems for functionals with a boundary integral
G Buttazzo, FP Maiale - arXiv preprint arXiv:2007.11317, 2020 - arxiv.org
We consider shape optimization problems for general integral functionals of the calculus of
variations that may contain a boundary term. In particular, this class includes optimization …
variations that may contain a boundary term. In particular, this class includes optimization …