Noticias en español
Nonexistence of positive supersolutions for semilinear fractional elliptic equations in exterior domains.
Abstract: In this talk, our goal is to investigate the nonexistence of positive solutions to nonlinear fractional elliptic inequalities in exterior domains of Rn, n ≥ 1. Our results extend the classical Liouville-type theorems of Gidas–Spruck [3] for semilinear elliptic equations, as well as the framework of Armstrong–Sirakov [1] for supersolutions of elliptic equations, to the nonlocal setting. They are also closely related to the fundamental solution approach of Felmer–Quaas [2] for nonlinear integral operators, although our arguments require substantial modifications to address the...
Read MoreOptimal Control of Sweeping Processes: Addressing the Challenge of Mixed Constraint.
Abstract: In the quest to model elastoplastic mechanical systems, J.J. Moreau introduced the concept of a ‘sweeping process’ in the 1970s. These systems are characterized by their dynamics, described by a discontinuous differential inclusion that can be expressed in terms of a cone, posing a unique challenge. This presentation delves into the complexities of establishing necessary optimality conditions for optimal control problems involving such dynamics, particularly when subject to mixed constraints on state and control variables. We will explore two distinct approaches to...
Read MoreCentral limit theorems for structured branching processes
Resumen: In this talk I will discuss recent progress on central limit theorems for supercritical branching Markov processes in infinite-dimensional settings. The class of processes under consideration allows for spatial dependence and branching mechanisms that need not be local. A key feature of our approach is that it only requires a fourth moment condition together with exponential convergence of the mean semigroup in a weighted total variation norm. This assumption is mild in that it does not rely on symmetry or detailed spectral information. The resulting central limit theorems capture...
Read MoreStrategyproof mechanisms without money for independence systems.
Abstract: We consider mechanisms without money for combinatorial independence systems. We are given an independence system where the ground set of items is partitioned into sets owned by strategic agents. Each item has a weight that is the private information of the agent owning it. A mechanism takes an independence system, the weights, and the partitioning as input and returns an independent set; it is strategyproof if no agent can increase the total weight of their items in the solution by reporting lower weights of their items to the mechanism or withholding a subset of their items from...
Read MoreDeformation to positive scalar curvature on complete manifolds with boundary.
Abstract: We will talk about conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics with positive scalar curvature and mean convex boundary.
Read MoreNew advances on the regularity of solutions to equations ruled by the $\infty$-Laplacian
Abstract: The theory of regularity, beyond its theoretical relevance in the study of partial differential equations, plays a central role in modeling various natural phenomena, including those arising in biology, materials science, fluid dynamics, and mathematical physics. In this talk, we will present results concerning the regularity of solutions to equations governed by the infinity Laplacian, with particular emphasis on infinity-harmonic functions, as well as recent advances on singular problems and Hénon-type equations.
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