Results 71 to 80 of about 3,355,987 (326)

Extended domain for fifth convergence order schemes

Cubo, 2021
We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations.
Ioannis K. Argyros, Santhosh George
doaj   +1 more source

Asymptotics of Hadamard Type for Eigenvalues of the Neumann Problem on $C^1$-domains for Elliptic Operators

, 2014
This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class $C^1$.
Thim, Johan
core   +1 more source

Geometric analysis for the metropolis algorithm on Lipschitz domains [PDF]

Inventiones mathematicae, 2010
This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original application of the Metropolis algorithm .
Diaconis, Persi, Lebeau, Gilles, Michel, Laurent   +2 more
openaire   +3 more sources

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, EarlyView.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source

Weyl asymptotics for Poincaré–Steklov eigenvalues in a domain with Lipschitz boundary [PDF]

, 2023
Grigori Rozenblum
openalex   +3 more sources

On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems [PDF]

, 2021
Pier Domenico Lamberti, Luigi Provenzano
openalex   +3 more sources

Global compact attractors and complete bounded trajectories for compressible magnetohydrodynamic system of equations [PDF]

Theoretical and Applied Mechanics
In this article, we investigate the global behavior of magnetohydrodynamic (MHD) fluid’s weak solutions in three-dimensional bounded domain with a compact Lipschitz boundary driven by arbitrary forces.
Muhammad Jan
doaj   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

Advances in Nonlinear Analysis, 2022
We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions,
Vitolo Antonio
doaj   +1 more source

Lipschitz extensions and approximations [PDF]

, 2020
The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditions are less restrictive and the extension is only required to be Lipschitz
V. Gutev
semanticscholar   +1 more source