Concept
Laplace operator
Related publications (149)
WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS
. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...
Amer Mathematical Soc2024Anisotropic Adaptive Finite Elements for a p-Laplacian Problem
Marco Picasso, Paride Passelli
The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...
Walter De Gruyter Gmbh2024Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems
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 ...
Lausanne2023Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds
Le Chen, Cheuk Yin Lee, David Jean-Michel Candil
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 ...
New York2023Fredholm transformation on Laplacian and rapid stabilization for the heat equation
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2022Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations
We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...
ELSEVIER SCIENCE SA2022Functional estimation of anisotropic covariance and autocovariance operators on the sphere
Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...
2022Nonsmooth and nonenergetic solutions of PDE’s through convex integration
In this Master thesis we explore the convex integration method by S. Müller and V. Šverák and its applications to partial differential equations. In particular, we use it to build very irregular solutions to elliptic systems. We also apply this method to b ...
2022A smooth basis for atomistic machine learning
Michele Ceriotti, Kevin Kazuki Huguenin-Dumittan, Filippo Bigi
Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...
AIP Publishing2022Fredholm transformation on Laplacian and rapid stabilization for the heat equations
We revisit the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption on the control operator, two scalar controls are necessary and sufficient ...
2021