Encontrados 20 documentos, a visualizar página 1 de 2

Stationary quasivariational inequalities with gradient constraint and nonhomoge...

Publicado em "From particle systems to partial differential equations. Part 2. (Springer proceedings in mathematics & statistics, vol. 75). ISBN 978-3-642-54270-1 ; We study existence of solution of stationary uasivariational inequalities with gradient constraint and nonhomogeneous boundary condition of Neumann or Dirichlet type. Through two different approaches, one making use of a fixed point theorem and th...

Variational and quasivariational inequalities with first order constraint

We study the existence of solutions of stationary variational and quasivariational inequalities with curl constraint, Neumann type boundary condition and a p-curl type operator. These problems are studied in bounded, not necessarily simply connected domains, with a special geometry, and the functional framework is the space of divergence-free functions with curl in $\boldsymbol L^p$ and null tangential or no...

Dynamics of a quasi-quadratic map

We consider the map $\cchi:\Q\to\Q$ given by $ \cchi(x)= x\ceil{x}$, where $\ceil{x}$ denotes the smallest integer greater than or equal to $x$, and study the problem of finding, for each rational, the smallest number of iterations by $\cchi$ that sends it into an integer. Given two natural numbers $M$ and $n$, we prove that the set of numerators of the irreducible fractions that have denominator$M$ and whos...

Multiplicador de Lagrange num problema com restrição não constante no gradiente

Prova-se a existência de solução, num sentido generalizado, de um problema com um multiplicador de Lagrange, para uma restrição arbitrária no gradiente e condição de Dirichlet homogénea na fronteira. Prova-se ainda a equivalência deste problema com a correspondente inequação variacional elíptica. A abordagem utilizada para provar o resultado de existência baseia-se na utilização de soluções de uma família aprox...

Um problema de grandes denominadores

Fixado $M\in \N$, escolhamos aleatoriamente $a_1\in \N$ e consideremos $M_1=\frac{M}{(M,a_1)}$. Repita-se este procedimento, seleccionando ao acaso $a_2$ e definindo $M_2=\frac{M_1}{(M_1,a_2)}$, e assim sucessivamente. Dados $M, n\in\N$, qual é a probabilidade, digamos $\mathcal{P}(n,M)$, de ser $M_n=1$? Tem-se $\mathcal{P}(1,M)=\frac{1}{M}$ e a relação de recorrência $\mathcal{P}(n+1,M)=\sum_{d; M}\frac{\varph...

Characteristic functions and averages

Em publicação ; Let $\Omega$ be a set and $\Omega_1,\ldots,\Omega_{m-1}$ subsets of $\Omega$, being $m$ an integer greater than one. For a given function $f=(f_1,\ldots f_m):\Omega\rightarrow\mathbb{R}^m$, we prove the existence of a unique function $\alpha=(\alpha_1,\ldots,\alpha_m):\Omega\rightarrow\mathbb{R}^m$ such that \begin{eqnarray*} \left\{ \begin{array}{lcl} \alpha_i & = & \alpha_{i+...

A diffusion problem with gradient constraint depending on the temperature

We consider a system of a variational inequality with gradient constraint depending on the temperature, coupled with the heat equation. We prove existence of solution of this system by approximating it by a system of equations and using a fixed point argument.

Research seminar on history and epistemology of mathematics : proceedings

The N-membranes problem with neumann boundary condition

We consider the problem of finding the equilibrium position of N membranes constrained not to pass through each other, under prescribed volumic forces and boundary tensions. This model corresponds to solve variationally a N-system for linear second order elliptic equations with sequential constraints. We obtain interior and boundary Lewy-Stampacchia type inequalities for the respective solution and we establish...

Remarks on the two and three membranes problem

We consider the problem of finding the equilibrium position of two or three membranes constrained not to pass through each other. For general linear second order elliptic operators with measurable coefficients we prove the Lewy-Stampacchia type inequalities and we establish sufficient conditions on the external forces to obtain the stability of the coincidence sets of the membranes, in analogy with the obstacle...