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Article
Learning, Mean Field Approximations, and Phase Transitions in Auction Models
In this paper, we study an agent-based model for multi-round, pay as bid, sealed bid reverse auctions using techniques from partial differential equations and statistical mechanics tools. We assume that in eac...
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Article
Non-local Equations and Optimal Sobolev Inequalities on Compact Manifolds
This paper deals with the theory of fractional Sobolev spaces on a compact Riemannian manifold (M, g). Our first main result shows that the fractional Sobolev spaces
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Article
Non-invasive study to determine changes in physical properties of multilayer materials
Exposure to different types of sources, such as electrical or thermal, can cause changes in the structure of materials, for example, cracks, stresses, oxidation, corrosion, among others. The goal of this work ...
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Article
Coupling Epidemiological Models with Social Dynamics
In this work we study a Susceptible-Infected-Susceptible model coupled with a continuous opinion dynamics model. We assume that each individual can take measures to reduce the probability of contagion, and the...
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Article
A Game Theoretic Model of Wealth Distribution
In this work, we consider an agent-based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero-sum game. Simultaneously, the agents update their way ...
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Article
The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem
In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solut...
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Article
Time dependent voiding mechanisms in polyamide 6 submitted to high stress triaxiality: experimental characterisation and finite element modelling
Double notched round bars made of semi-crystalline polymer polyamide 6 (PA6) were submitted to monotonic tensile and creep tests. The two notches had a root radius of 0.45 mm, which imposes a multiaxial stress...
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Article
Local existence conditions for an equations involving the \({{\varvec{p}}}({{\varvec{x}}})\) -Laplacian with critical exponent in \({\mathbb {R}}^N\)
The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in
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Article
The limit as \(p\rightarrow \infty \) in the eigenvalue problem for a system of p-Laplacians
In this paper, we study the behavior as \(p\rightarrow \infty \) ...
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Article
On the Sobolev trace Theorem for variable exponent spaces in the critical range
In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give lo...
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Article
Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds
We describe the asymptotic behaviour in Sobolev spaces of sequences of solutions of Paneitz-type equations [Eq. (E α ) below] on a compact Riemannian man...
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Article
Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality $$S\|u\|_{L^{p_*}(\partial\Omega)}^p...
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Article
Blow-up theory for symmetric critical equations involving the p-Laplacian
We describe in this paper the asymptotic behaviour in Sobolev spaces of sequences of solutions of critical equations involving the p-Laplacian (see equations (E α) below) on a comp...
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Article
Stability and perturbations of the domain for the first eigenvalue of the 1-Laplacian
We study the dependence of the first eigenvalue of the 1-Laplacian with respect to perturbations of the domain. We provide results ranging from general type of perturbations to regular perturbations by diffeom...
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Article
Asymptotic estimates and blow-up theory for critical equations involving the p-Laplacian
We prove the SH1 p —theory for critical equations involving the p-Laplace operator on compact manifolds. We also prove pointwise estimates for these equations.
