Concept

Fréchet derivative

Publications associées (30)

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 ...

American Mathematical Society (AMS)2023

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Semiclassical methods in conformal field theories scrutinized by the epsilon-expansion

Gil Badel

Conformal Field Theories (CFTs) are crucial for our understanding of Quantum Field Theory (QFT). Because of their powerful symmetry properties, they play the role of signposts in the space of QFTs. Any method that gives us information about their structure ...

EPFL2022

Global bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frech ...

2021

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Robert Dalang

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

INST MATHEMATICAL STATISTICS-IMS2021

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...

2020

On design strategies for binary dielectric metasurfaces based on the Fourier modal method

Kévin Müller

Binary dielectric metasurfaces are arrays of sub-wavelength structures that act as a thin layer of artificial material. They are generally lossless and relatively simple to fabricate since only a single structuring step is required. By carefully designing ...

EPFL2020

Radiative Backpropagation: An Adjoint Method for Lightning-Fast Differentiable Rendering

Wenzel Alban Jakob, Merlin Eléazar Nimier-David, Sébastien Nicolas Speierer

Physically based differentiable rendering has recently evolved into a powerful tool for solving inverse problems involving light. Methods in this area perform a differentiable simulation of the physical process of light transport and scattering to estimate ...

ASSOC COMPUTING MACHINERY2020

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Boris Buffoni

We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) x R-2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of ...

MATHEMATICAL SCIENCE PUBL2019

Complex magnetoelectric effect in multiferroic composites: the case of PFN- PT/(Co,Ni)Fe2O4

We report a systematic study of the magnetoelectric (ME) voltage coefficient as a complex quantity in the particulate composite of ferroelectric solid solution 0.94Pb(Fe1/2N1/2)O-3-0.06PbTiO(3)(PFN-PT) with CoFe2O4(CFO) and NiFe2O4 (NFO) ferrites. The resu ...

2019

Criteria for the existence of a potential well

Charles Stuart

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017

Fréchet means in Wasserstein space : theory and algorithms

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

A Sampling Theory for Non-Decaying Signals

Michaël Unser, Quy Ha Nguyen

The classical assumption in sampling and spline theories is that the input signal is square-integrable, which prevents us from applying such techniques to signals that do not decay or even grow at infinity. In this paper, we develop a sampling theory for m ...

2017

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

Michaël Unser, Julien René Fageot, John Paul Ward

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

2017

Contributions to Modelling Extremes of Spatial Data

Linda Frossard

The increasing interest in using statistical extreme value theory to analyse environmental data is mainly driven by the large impact extreme events can have. A difficulty with spatial data is that most existing inference methods for asymptotically justifie ...

EPFL2017

On the geometrical interpretation of scale-invariant models of inflation

Georgios Karananas, Javier Rubio

We study the geometrical properties of scale-invariant two-field models of inflation. In particular, we show that when the field-derivative space in the Einstein frame is maximally symmetric during inflation, the inflationary predictions can be universal a ...

Elsevier2016

Simultaneous estimation of phase and its pth order derivatives

Pramod Rastogi, Rishikesh Dilip Kulkarni

One unaddressed challenge in optical metrology has been the measurement of higher order derivatives of rough specimens subjected to loading. In this paper, we investigate an approach that allows for the simultaneous estimation of the phase and its higher o ...

2016

Bifurcation points of a singular boundary-value problem on (0,1)

Charles Stuart

Following earlier work on some special cases [17,11] and on the analogous problem in higher dimensions [10,20], we make a more thorough investigation of the bifurcation points for a nonlinear boundary value problem of the form -{A(x)u' (x)}'.= f (lambda, x ...

Academic Press Inc Elsevier Science2016

Bifurcation without Frechet differentiability at the trivial solution

Charles Stuart

Criteria for the bifurcation of small solutions of an equation F(lambda,u) = 0 from a line {(lambda,0): lambda is an element of R} of trivial solutions are usually based on properties of the DuF(lambda,0) at the trivial solutions, where the partial derivat ...

Wiley-Blackwell2015

Bifurcation at isolated singular points for a degenerate elliptic eigenvalue problem

Charles Stuart

We consider bifurcation from the line of trivial solutions for a nonlinear eigenvalue problem on a bounded open subset, Omega, of R-N with N >= 3, containing 0. The leading term is a degenerate elliptic operator of the form L(u) = del . A del u where A is ...

Pergamon-Elsevier Science Ltd2015

Publications associées (30)

INST MATHEMATICAL STATISTICS-IMS2021

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017