Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

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Non-normal forms

Yves-Marie François Ducimetière

In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...

EPFL2024

Anomalous dissipation and other non-smooth phenomena in fluids

Massimo Sorella

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Fernando José Henriquez Barraza

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

Springer Birkhauser2024

Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

2023

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

Amer Mathematical Soc2023

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, David Jean-Michel Candil, Cheuk Yin Lee

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

Springer2023

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Rafael Vazquez Hernandez

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

Espen Sande

We present outlier-free isogeometric Galerkin discretizations of eigenvalue problems related to the biharmonic and the polyharmonic operator in the univariate setting. These are Galerkin discretizations in certain spline subspaces that provide accurate app ...

Elsevier Science Sa2023

The hunt for the Karman 'constant' revisited

Peter Monkewitz

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on th ...

Cambridge University Press2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

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