Some New Results On Differential Inclusions For Differential Forms

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Biological and living organisms sense and process information from their surroundings, typically having access only to a subset of external observables for a limited amount of time. In this Letter, we uncover how biological systems can exploit these access ...

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS (sums of squares) ...

The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...

Let Omega subset of R-n be an open set, A is an element of R-nxn and G : Omega -> R-nxn be given. We look for a solution u : Omega -> R-n of the equation ...

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of th ...

Given a planar domain Omega, we study the Dirichlet problem {-divA(x, del v) = f in Omega, v = 0 on partial derivative Omega, where the higher-order term is a quasilinear elliptic operator, and f belongs to the Zygmund space L(log L)delta(log log log L)(be ...

Let parallel to.parallel to be a norm in R-d whose unit ball is B. Assume that V subset of B is a finite set of cardinality n, with Sigma(v is an element of V) v = 0. We show that for every integer k with 0

Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...

We study integrals of the form integral(Omega) f (d omega), where 1

This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form

\mathcal Lu + \mathcal Q(u) = f.

The main result of thi ...

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 ...

This paper is concerned with the mathematical analysis of a coupled elliptic–parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction–diffus ...

In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n is an element of N a priori known, separated microscopic length scales, are considered. The convergence of multileve ...

In Control System Theory, the study of continuous-time, finite dimensional, underdetermined systems of ordinary differential equations is an important topic. Classification of systems in different categories is a natural initial step to the analysis of a g ...

In this paper, we consider nonlinear Schrodinger equations of the following type: -Delta u(x) + V (x) u(x) -q(x)|u(x)|sigma u(x) =lambda u(x), x is an element of R-N, u is an element of H-1(R-N) \ {0}, where N >= 2 and sigma > 0. We concentrate on situatio ...

The objective of this work is to develop a numerical framework to perform rapid and reliable simulations for solving parametric problems in domains represented by networks and to extend the classical reduced basis method. Aimed at this scope, we propose tw ...

Let {X(t), t is an element of R-N} be a fractional Brownian motion in R-d of index H. If L(0,I) is the local time of X at 0 on the interval I subset of R-N, then there exists a positive finite constant c(=c(N,d,H)) such that ...

Some New Results On Differential Inclusions For Differential Forms

Chat with Graph Search

Tuning Transduction from Hidden Observables to Optimize Information Harvesting

The first Grushin eigenvalue on cartesian product domains

Stokes, Gibbs, and Volume Computation of Semi-Algebraic Sets

Packing the Boolean lattice with copies of a poset

On the equation A del u plus (del u)(t) A = G

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Calculus of Variations for Differential Forms

Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

Small subset sums

Optimal transport of closed differential forms for convex costs

Calculus of variations with differential forms

Application aux équations aux dérivées partielles d'une méthode par point fixe et le problème des deux puits

Bifurcation without Frechet differentiability at the trivial solution

Solvability analysis and numerical approximation of linearized cardiac electromechanics

Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs

Finite Dimensional Methods for Differential Flatness

Odd linking and bifurcation in gaps: the weakly indefinite case

Reduced Basis Methods for the Solution of Parametrized PDEs in Repetitive and Complex Networks with Application to CFD

The Exact Hausdorff Measure of the Zero Set of Fractional Brownian Motion