Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Curve packing and modulus estimates
2018
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.
Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations
2015
In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth \[ \begin{cases} -\Delta_{p}u-{\displaystyle \frac{\mu}{|x|^{p}}|u|^{p-2}u}{\displaystyle =\frac{|u|^{\frac{(N-s)p}{N-p}-2}u}{|x|^{s}}}+\lambda|u|^{p-2}u & \text{in }B,\\ u=0 & \text{on }\partial B, \end{cases} \] where $B$ is an open finite ball in $\mathbb{R}^{N}$ centered at the origin, $1<p<N$, $-\infty<\mu<((N-p)/p)^{p}$, $0\le s<p$ and $\lambda\in\mathbb{R}$. A related limiting problem is also considered.
A Quantitative Analysis of Metrics on Rn with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows
2017
We prove a quantitative structure theorem for metrics on $\mathbf{R}^n$ that are conformal to the flat metric, have almost constant positive scalar curvature, and cannot concentrate more than one bubble. As an application of our result, we show a quantitative rate of convergence in relative entropy for a fast diffusion equation in $\mathbf{R}^n$ related to the Yamabe flow.
Mappings of Finite Distortion : Compactness of the Branch Set
2017
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n - 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound. Peer reviewed
Some notes on a superlinear second order Hamiltonian system
2016
Variational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered.
Non-Local Scattering Kernel and the Hydrodynamic Limit
2007
In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.
A non-linear stochastic approach of ligaments and tendons fractional-order hereditariness
2020
Abstract In this study the non-linear hereditariness of knee tendons and ligaments is framed in the context of stochastic mechanics. Without losing the possibility of generalization, this work was focused on knee Anterior Cruciate Ligament (ACL) and the tendons used in its surgical reconstruction. The proposed constitutive equations of fibrous tissues involves three material parameters for the creep tests and three material parameters for relaxation tests. One-to-one relations among material parameters estimated in creep and relaxations were established and reported in the paper. Data scattering, observed with a novel experimental protocol used to characterize the mechanics of the tissue, w…
On the moving multi-loads problem in discontinuous beam structures with interlayer slip
2017
Abstract This contribution proposes an efficient approach to the moving multi-loads problem on two-layer beams with interlayer slip and elastic translational supports. The Euler-Bernoulli hypothesis is assumed to hold for each layer separately, and a linear constitutive relation between the horizontal slip and the interlaminar shear force is considered. It is shown that, using the theory of generalized functions to treat the discontinuous response variables, exact eigenfunctions can be derived from a characteristic equation built as determinant of a 6 x 6 matrix. Building pertinent orthogonality conditions for the deflection eigenfunctions, a closed-form analytical response is established i…
Explicit closed form solutions of boundary value problems for systems of difference equations
1990
In this paper boundary value problems for systems of difference equations of the type , where A j ∈ C p×p and bn y j+n ∈ C p , for 0≤j≤k − 1, are studied from an algebraic point of view. Existence conditions and closed form solutions are given in terms of co-solutions of the algebraic matrix equation .
Generalized inverse of the compliance tensor, and behaviour of incompressible anisotropic materials - Application to damage
1997
Before the final rupture, most structural materials exhibit an import damage in the form of microvoids. The overall behaviour of a damaged elastic material depends on the void volume fraction f. Undamaged polymers are generally considered as incompressible elastic. Metals at high temperature may be considered as linearly viscoplastic. Thus the undamaged material may be described by an incompressible behaviour, while the overall behaviour of the damaged material is compressible depending on the void volume fraction. The transition from a compressible to an incompressible behaviour leads to a singular compliance matrix and an undefined rigidity matrix. The generalized inverse of the complianc…